Finite Group Databasebeta

← D3×#5115 #11866746

Subgroups — D3×#5115 #11866746

Order 1152.

1299 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×C8C211yesmaximal, characteristic, complemented
2D3×#930C212yesmaximal, complemented
3C2×D3×D24C211yesmaximal, characteristic, complemented
4#10592814C211yesmaximal, characteristic, complemented
5C3×#5115C211yesmaximal, characteristic, complemented
6#10591164C212yesmaximal, complemented
7D3×#821C212yesmaximal, complemented
8#10590832C211yesmaximal, characteristic, complemented
9#10590831C211yesmaximal, characteristic, complemented
10#10590826C212yesmaximal, complemented
11D3×#818C211yesmaximal, characteristic, complemented
12C2×#5115—31nomaximal
13D3×#466—31nomaximal
14C22×C3×C4×D3C2211yescharacteristic
15C2×D3×#67—22no—
16C2×D3×D12C2212yes—
17C22×C32×C8C2211yescharacteristic, complemented
18#64139C2212yescomplemented
19C2×#3745C2211yescharacteristic, complemented
20C3×#930C2212yescomplemented
21C22×C3×C3⋊C8C2211yescharacteristic, complemented
22C2×C3×D24C2211yescharacteristic, complemented
23C2×C3×D3×C8—24no—
24C2×C3×D3×C8C2211yescharacteristic
25C2×C3×D3×C8C2211yescharacteristic
26C2×C3×D3×C8C2211yescharacteristic, complemented
27C2×C3×D3×C8C2211yescharacteristic, complemented
28#63978—22no—
29D3×(C2×D3)⋊C4—22no—
30#63909C2212yescomplemented
31#63908C2212yescomplemented
32#63906—22no—
33D3×C4⋊Dic3C2212yes—
34C2×#3714C2212yescomplemented
35D3×D24—24no—
36#63648C2212yescomplemented
37#63645C2211yescharacteristic, complemented
38C3×#821C2212yescomplemented
39C3×#818C2211yescharacteristic, complemented
40#63575C2212yescomplemented
41#63564C2212yescomplemented
42#63563C2212yescomplemented
43C23×C3×C8—31no—
44C2×#930—32no—
45C2×D3×D8—31no—
46C22×D24—31no—
47C22×D3×C8D311yescharacteristic, complemented
48D3×#121—32no—
49C3×#466—31no—
50#5157—31no—
51#5115—31no—
52#5115—31no—
53#5115—32no—
54#5115—31no—
55#5115—32no—
56#5115—31no—
57#5115—61no—
58#5115D311yescharacteristic, direct product factor
59C2×#821—32no—
60C2×#818—31no—
61#5038—32no—
62#4883—31no—
63D3×#107—31no—
64#4775—32no—
65D3×#102—32no—
66C23×C3×D3D411yescharacteristic
67C22×D32—22no—
68C22×C32×C4C2311yescharacteristic
69C2×#638—22no—
70C2×C4⋊(C3⋊D3)C2312yes—
71C2×C3×#67—22no—
72C22×C3×Dic3D411yescharacteristic
73C2×C3×D12C2312yes—
74C2×C3×C4×D3—22no—
75C2×C3×C4×D3—22no—
76C2×C3×C4×D3D411yescharacteristic
77C2×C3×C4×D3D411yescharacteristic
78C2×C3×C4×D3C2311yescharacteristic
79C2×C3×C4×D3C2311yescharacteristic
80D3×#67—48no—
81C2×#626—22no—
82C2×#626—22no—
83C2×#625—22no—
84C2×D3×Dic3—22no—
85D3×D12—24no—
86D3×D12—24no—
87C2×C32×C8—22no—
88C2×C32×C8C2311yescharacteristic
89C2×C32×C8C2311yescharacteristic
90#3752—22no—
91C4⋊(C3⋊Dic3)C2312yes—
92#3745—22no—
93C3×(C2×D3)⋊C4—22no—
94C3×C4⋊Dic3C2312yes—
95C2×C3×C3⋊C8—22no—
96C2×C3×C3⋊C8C2311yescharacteristic
97C2×C3×C3⋊C8C2311yescharacteristic
98C3×D24—22no—
99C3×D3×C8—22no—
100C3×D3×C8—22no—
101C3×D3×C8—22no—
102C3×D3×C8D414yescomplemented
103Dic3⋊Dic3—22no—
104#3722—22no—
105(C2×D3)⋊Dic3—22no—
106#3714—24no—
107C2×#466—91noSylow
108C23×C3×C4—31no—
109C22×#67—62no—
110C2×D3×D4—32no—
111C2×D3×D4—62no—
112C22×D12—32no—
113C22×C4×D3C2×D311yescharacteristic
114C2×C3×D8—31no—
115C22×C3×C8—21no—
116C22×C3×C8—31no—
117C22×C3×C8—31no—
118C22×C3×C8—31no—
119C22×C3×C8—31no—
120C22×C3×C8—31no—
121C22×C3×C8—64no—
122C22×C3×C8C2×D311yescharacteristic, complemented
123C22×C3×C8C2×D311yescharacteristic, complemented
124C3×#121—32no—
125#939—62no—
126#938—32no—
127C2×#213—32no—
128#930—32no—
129#930—32no—
130#930—32no—
131#930—32no—
132#930—62no—
133#930—62no—
134#930—62no—
135#930C2×D312yescomplemented
136C2×(C2×D3)⋊C4—62no—
137C2×C4⋊Dic3—32no—
138C22×C3⋊C8C2×D311yescharacteristic, complemented
139D3×D8—64no—
140C2×D24—32no—
141C2×D24—31no—
142C2×D24—31no—
143C2×D24—61no—
144C2×D24—64no—
145C2×D24C2×D311yescharacteristic, complemented
146C2×D3×C8—24no—
147C2×D3×C8C2×D311yescharacteristic
148C2×D3×C8C2×D311yescharacteristic
149C2×D3×C8C2×D311yescharacteristic, complemented
150C2×D3×C8C2×D311yescharacteristic, complemented
151#895—32no—
152D3×C4⋊C4—32no—
153#884—62no—
154D3×C22⋊C4—62no—
155C3×#107—31no—
156C3×#102—32no—
157#832—32no—
158#821—32no—
159#821—32no—
160#821—32no—
161#821—32no—
162#821—62no—
163#821C2×D312yescomplemented
164#818—31no—
165#818—31no—
166#818—32no—
167#818—61no—
168#818C2×D311yescharacteristic, complemented
169#809—32no—
170#807—32no—
171C23×C32C2×D411yescharacteristic
172C22×C3⋊D3—22no—
173C22×C3×D3—22no—
174C22×C3×D3—22no—
175C22×C3×D3—22no—
176C22×C3×D3D814yescomplemented
177C22×C3×D3C2×D411yescharacteristic
178C22×C3×D3C2×D411yescharacteristic
179C2×D32—44no—
180C2×D32—44no—
181C2×D32—44no—
182C2×C32×C4—21no—
183C2×C32×C4—21no—
184C2×C32×C4C2×D411yescharacteristic
185C2×C32×C4C2411yescharacteristic
186#638—44no—
187C2×C3⋊Dic3—22no—
188C4⋊(C3⋊D3)—22no—
189C4⋊(C3⋊D3)—22no—
190C3×#67—44no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3C2×D411yescharacteristic
194C2×C3×Dic3C2×D411yescharacteristic
195C3×D12—22no—
196C3×D12—22no—
197C3×C4×D3—22no—
198C3×C4×D3—21no—
199C3×C4×D3—21no—
200C3×C4×D3—22no—
201C3×C4×D3C2×D412yes—
202C3×C4×D3#4112yes—
203#626—44no—
204#626—44no—
205#625—44no—
206D3×Dic3—44no—
207C32×C8—21no—
208C32×C8C2×D412yescomplemented
209C3×C3⋊C8—21no—
210C3×C3⋊C8C2×D412yescomplemented
211C22×D8—91no—
212C23×C8—31no—
213C2×#121—92no—
214#466—31no—
215#466—92no—
216#466—91no—
217#466—92no—
218#466—91no—
219#466—91no—
220C2×#107—91no—
221C2×#102—92no—
222C24×C3—31no—
223C23×D3—62no—
224C23×D3—62no—
225C23×D3D1211yescharacteristic
226C2×C3×D4—32no—
227C2×C3×D4—62no—
228C22×C3×C4—21no—
229C22×C3×C4—31no—
230C22×C3×C4—31no—
231C22×C3×C4—31no—
232C22×C3×C4—31no—
233C22×C3×C4—31no—
234C22×C3×C4—62no—
235C22×C3×C4—62no—
236C22×C3×C4C22×D311yescharacteristic
237C22×C3×C4C22×D311yescharacteristic
238C2×#67—22no—
239C2×#67—62no—
240C2×#67—62no—
241C2×#67—62no—
242C2×#67—62no—
243C2×#67—62no—
244C2×#67—62no—
245C2×#67—122no—
246C2×#67—128no—
247C22×Dic3—62no—
248C22×Dic3D1211yescharacteristic
249D3×D4—64no—
250D3×D4—64no—
251D3×D4—128no—
252C2×D12—32no—
253C2×D12—32no—
254C2×D12—62no—
255C2×D12—64no—
256C2×D12—64no—
257C2×D12—62no—
258C2×D12—62no—
259C2×D12C22×D312yes—
260C2×C4×D3—22no—
261C2×C4×D3—22no—
262C2×C4×D3—62no—
263C2×C4×D3D1211yescharacteristic
264C2×C4×D3D1211yescharacteristic
265C2×C4×D3C22×D311yescharacteristic
266C2×C4×D3C22×D311yescharacteristic
267C3×D8—62no—
268C2×C3×C8—22no—
269C2×C3×C8—22no—
270C2×C3×C8—21no—
271C2×C3×C8—21no—
272C2×C3×C8—31no—
273C2×C3×C8—34no—
274C2×C3×C8—31no—
275C2×C3×C8—42no—
276C2×C3×C8—62no—
277C2×C3×C8—62no—
278C2×C3×C8—62no—
279C2×C3×C8—62no—
280C2×C3×C8C22×D311yescharacteristic
281C2×C3×C8C22×D311yescharacteristic
282C2×C3×C8C22×D311yescharacteristic
283C2×C3×C8C22×D311yescharacteristic
284C3×C4⋊C4—32no—
285C3×C22⋊C4—62no—
286#217—62no—
287#213—64no—
288(C2×D3)⋊C4—22no—
289(C2×D3)⋊C4—62no—
290(C2×D3)⋊C4—62no—
291(C2×D3)⋊C4—62no—
292(C2×D3)⋊C4—62no—
293(C2×D3)⋊C4—62no—
294(C2×D3)⋊C4—122no—
295C4⋊Dic3—32no—
296C4⋊Dic3—32no—
297C4⋊Dic3—62no—
298C4⋊Dic3—62no—
299C4⋊Dic3C22×D312yes—
300Dic3⋊C4—62no—
301C2×C3⋊C8—22no—
302C2×C3⋊C8C22×D311yescharacteristic
303C2×C3⋊C8C22×D311yescharacteristic
304D24—22no—
305D24—64no—
306D24—62no—
307D24—62no—
308D24—122no—
309D3×C8—22no—
310D3×C8—22no—
311D3×C8—22no—
312D3×C8#6714yescomplemented
313C22×C32—21no—
314C22×C32—21no—
315C22×C32C2×D812yescomplemented
316C22×C32C22×D411yescharacteristic
317C2×C3⋊D3—42no—
318C2×C3⋊D3—42no—
319C2×C3⋊D3—42no—
320C2×C3×D3—21no—
321C2×C3×D3—21no—
322C2×C3×D3—28no—
323C2×C3×D3—42no—
324C2×C3×D3—42no—
325C2×C3×D3—42no—
326C2×C3×D3#12112yes—
327C2×C3×D3C2×D812yes—
328C2×C3×D3C2×D812yescomplemented
329C2×C3×D3#13512yes—
330D32—88no—
331C32×C4—21no—
332C32×C4C22×D411yescharacteristic
333C32×C4C2×#4111yescharacteristic
334C3⋊Dic3—42no—
335C3×Dic3—21no—
336C3×Dic3—42no—
337C3×Dic3#12112yes—
338C22×D4—92no—
339C22×D4—182no—
340C23×C4—31no—
341C2×D8—31no—
342C2×D8—92no—
343C2×D8—91no—
344C2×D8—184no—
345C22×C8—31no—
346C22×C8—31no—
347C22×C8—31no—
348C22×C8—31no—
349C22×C8—31no—
350C22×C8—64no—
351C22×C8D3211yescharacteristic, complemented
352#121—32no—
353#121—92no—
354#121—92no—
355#121—92no—
356#121—182no—
357#121—182no—
358C2×C4⋊C4—92no—
359C2×C22⋊C4—182no—
360#107—31no—
361#107—92no—
362#107—91no—
363#102—32no—
364#102—92no—
365#102—92no—
366#102—92no—
367C23×C3—21no—
368C23×C3—31no—
369C23×C3—34no—
370C23×C3—31no—
371C23×C3—62no—
372C23×C3—62no—
373C23×C3—62no—
374C23×C3C2×D1211yescharacteristic
375C23×C3D3×D411yescharacteristic
376C22×D3—22no—
377C22×D3—22no—
378C22×D3—22no—
379C22×D3—62no—
380C22×D3—62no—
381C22×D3—122no—
382C22×D3—124no—
383C22×D3—124no—
384C22×D3—124no—
385C22×D3—124no—
386C22×D3—124no—
387C22×D3—124no—
388C22×D3D2414yescomplemented
389C22×D3C2×D1211yescharacteristic
390C22×D3C2×D1211yescharacteristic
391C3×D4—62no—
392C3×D4—62no—
393C3×D4—124no—
394C2×C3×C4—21no—
395C2×C3×C4—21no—
396C2×C3×C4—21no—
397C2×C3×C4—21no—
398C2×C3×C4—21no—
399C2×C3×C4—21no—
400C2×C3×C4—31no—
401C2×C3×C4—32no—
402C2×C3×C4—32no—
403C2×C3×C4—31no—
404C2×C3×C4—41no—
405C2×C3×C4—41no—
406C2×C3×C4—62no—
407C2×C3×C4—62no—
408C2×C3×C4—62no—
409C2×C3×C4—61no—
410C2×C3×C4—61no—
411C2×C3×C4—62no—
412C2×C3×C4C2×D1211yescharacteristic
413C2×C3×C4D3×D411yescharacteristic
414C2×C3×C4C23×D311yescharacteristic
415C2×C3×C4C23×D311yescharacteristic
416#67—44no—
417#67—124no—
418#67—124no—
419#67—124no—
420#67—124no—
421#67—124no—
422#67—124no—
423#67—244no—
424C2×Dic3—22no—
425C2×Dic3—22no—
426C2×Dic3—62no—
427C2×Dic3—62no—
428C2×Dic3—122no—
429C2×Dic3—124no—
430C2×Dic3C2×D1211yescharacteristic
431C2×Dic3C2×D1211yescharacteristic
432D12—22no—
433D12—22no—
434D12—62no—
435D12—62no—
436D12—62no—
437D12—62no—
438D12—122no—
439D12—122no—
440D12—124no—
441D12—124no—
442C4×D3—22no—
443C4×D3—21no—
444C4×D3—21no—
445C4×D3—22no—
446C4×D3—124no—
447C4×D3#23512yes—
448C4×D3C2×#6712yes—
449C3×C8—21no—
450C3×C8—21no—
451C3×C8—22no—
452C3×C8—32no—
453C3×C8—41no—
454C3×C8—61no—
455C3×C8D3×D412yescomplemented
456C3×C8C2×#6712yescomplemented
457C3⋊C8—21no—
458C3⋊C8C2×#6712yescomplemented
459C2×C32—22no—
460C2×C32C2×#12111yescharacteristic
461C2×C32C22×D811yescharacteristic
462C2×C32C2×#13511yescharacteristic
463C3⋊D3—82no—
464C3×D3—22no—
465C3×D3—82no—
466C3×D3#46614yescomplemented
467C24—31no—
468C24—182no—
469C2×D4—32no—
470C2×D4—62no—
471C2×D4—92no—
472C2×D4—184no—
473C2×D4—184no—
474C2×D4—182no—
475C2×D4—182no—
476C2×D4—182no—
477C2×D4—182no—
478C2×D4—368no—
479C22×C4—31no—
480C22×C4—31no—
481C22×C4—31no—
482C22×C4—31no—
483C22×C4—31no—
484C22×C4—62no—
485C22×C4—62no—
486C22×C4—182no—
487C22×C4C2×D3211yescharacteristic
488D8—62no—
489D8—184no—
490D8—182no—
491C2×C8—22no—
492C2×C8—31no—
493C2×C8—34no—
494C2×C8—31no—
495C2×C8—62no—
496C2×C8—62no—
497C2×C8—62no—
498C2×C8—62no—
499C2×C8C2×D3211yescharacteristic
500C2×C8C2×D3211yescharacteristic
501C4⋊C4—32no—
502C4⋊C4—92no—
503C4⋊C4—182no—
504C22⋊C4—62no—
505C22⋊C4—182no—
506C22⋊C4—182no—
507C22⋊C4—182no—
508C22×C3—21no—
509C22×C3—21no—
510C22×C3—21no—
511C22×C3—21no—
512C22×C3—21no—
513C22×C3—22no—
514C22×C3—32no—
515C22×C3—32no—
516C22×C3—32no—
517C22×C3—32no—
518C22×C3—41no—
519C22×C3—41no—
520C22×C3—68no—
521C22×C3—61no—
522C22×C3—61no—
523C22×C3—122no—
524C22×C3—122no—
525C22×C3—122no—
526C22×C3C2×D2412yescomplemented
527C22×C3D3×D812yescomplemented
528C22×C3C22×D1211yescharacteristic
529C22×C3C2×D3×D411yescharacteristic
530C2×D3—21no—
531C2×D3—21no—
532C2×D3—28no—
533C2×D3—42no—
534C2×D3—42no—
535C2×D3—42no—
536C2×D3—122no—
537C2×D3—122no—
538C2×D3—122no—
539C2×D3—122no—
540C2×D3—122no—
541C2×D3—122no—
542C2×D3—242no—
543C2×D3—242no—
544C2×D3—242no—
545C2×D3—248no—
546C2×D3—248no—
547C2×D3C2×D2412yes—
548C2×D3C2×D2412yescomplemented
549C2×D3#90412yes—
550C2×D3#93012yes—
551C3×C4—21no—
552C3×C4—21no—
553C3×C4—21no—
554C3×C4—21no—
555C3×C4—32no—
556C3×C4—41no—
557C3×C4—61no—
558C3×C4—122no—
559C3×C4C2×#23511yescharacteristic
560C3×C4C2×D3×D411yescharacteristic
561C3×C4D3×#4111yescharacteristic
562C3×C4C22×#6711yescharacteristic
563Dic3—21no—
564Dic3—42no—
565Dic3—122no—
566Dic3—122no—
567Dic3—242no—
568Dic3#93012yes—
569C32C2×#46611yescharacteristic, complemented, Sylow
570C23—31no—
571C23—31no—
572C23—34no—
573C23—62no—
574C23—62no—
575C23—62no—
576C23—182no—
577C23—364no—
578C23—364no—
579C23—364no—
580C23D3×D1211yescharacteristic
581D4—62no—
582D4—62no—
583D4—124no—
584D4—182no—
585D4—182no—
586D4—364no—
587D4—364no—
588D4—364no—
589D4—364no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—31no—
593C2×C4—32no—
594C2×C4—32no—
595C2×C4—31no—
596C2×C4—62no—
597C2×C4—62no—
598C2×C4—62no—
599C2×C4—61no—
600C2×C4—61no—
601C2×C4—62no—
602C2×C4—182no—
603C2×C4—364no—
604C2×C4D3×D1211yescharacteristic
605C2×C4C22×D3211yescharacteristic
606C8—21no—
607C8—32no—
608C8—61no—
609C8D3×#6712yescomplemented
610C2×C3—22no—
611C2×C3—22no—
612C2×C3—21no—
613C2×C3—21no—
614C2×C3—21no—
615C2×C3—34no—
616C2×C3—42no—
617C2×C3—62no—
618C2×C3—242no—
619C2×C3D3×#12111yescharacteristic
620C2×C3C22×D2411yescharacteristic
621C2×C3C2×#90411yescharacteristic
622C2×C3C2×D3×D811yescharacteristic
623C2×C3D3×#13511yescharacteristic
624C2×C3C2×#93011yescharacteristic
625D3—22no—
626D3—82no—
627D3—242no—
628D3—242no—
629D3—482no—
630D3#511514yesdirect product factor
631C22—21no—
632C22—21no—
633C22—32no—
634C22—32no—
635C22—32no—
636C22—32no—
637C22—68no—
638C22—61no—
639C22—61no—
640C22—122no—
641C22—122no—
642C22—122no—
643C22—362no—
644C22—362no—
645C22—362no—
646C22—728no—
647C22D3×D2412yescomplemented
648C22C2×D3×D1211yescharacteristic
649C4—21no—
650C4—32no—
651C4—61no—
652C4—122no—
653C4—362no—
654C4D3×#23511yescharacteristic
655C4C2×D3×#6711yescharacteristic
656C3—21no—
657C3D3×#46611yescharacteristic, complemented
658C3C2×#511511yescharacteristic, complemented
659C2—22no—
660C2—34no—
661C2—62no—
662C2—242no—
663C2—722no—
664C2C2×D3×D2411yescharacteristic
665C2D3×#90411yescharacteristic
666C2D3×#93011yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
hypercenterC22×C8D32
hypocenterC32C2×#466
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×C3×D3×C8C2semidirect
2. D3×#930C2semidirect
3. C2×D3×D24C2semidirect
4. #10592814C2semidirect
5. C3×#5115C2semidirect
6. #10591164C2semidirect
7. D3×#821C2semidirect
8. #10590832C2semidirect
9. #10590831C2semidirect
10. #10590826C2semidirect
11. D3×#818C2semidirect
17. C22×C32×C8C22semidirect
18. #64139C22semidirect
19. C2×#3745C22semidirect
20. C3×#930C22semidirect
21. C22×C3×C3⋊C8C22semidirect
22. C2×C3×D24C22semidirect
26. C2×C3×D3×C8C22semidirect
27. C2×C3×D3×C8C22semidirect
30. #63909C22semidirect
31. #63908C22semidirect
34. C2×#3714C22semidirect
36. #63648C22semidirect
37. #63645C22semidirect
38. C3×#821C22semidirect
39. C3×#818C22semidirect
40. #63575C22semidirect
41. #63564C22semidirect
42. #63563C22semidirect
47. C22×D3×C8D3semidirect
58. #5115D3direct (N × H)
102. C3×D3×C8D4semidirect
122. C22×C3×C8C2×D3semidirect
123. C22×C3×C8C2×D3semidirect
135. #930C2×D3semidirect
138. C22×C3⋊C8C2×D3semidirect
145. C2×D24C2×D3semidirect
149. C2×D3×C8C2×D3semidirect
150. C2×D3×C8C2×D3semidirect
163. #821C2×D3semidirect
168. #818C2×D3semidirect
176. C22×C3×D3D8semidirect
208. C32×C8C2×D4semidirect
210. C3×C3⋊C8C2×D4semidirect
312. D3×C8#67semidirect
315. C22×C32C2×D8semidirect
328. C2×C3×D3C2×D8semidirect
351. C22×C8D32semidirect
388. C22×D3D24semidirect
455. C3×C8D3×D4semidirect
456. C3×C8C2×#67semidirect
458. C3⋊C8C2×#67semidirect
466. C3×D3#466semidirect
526. C22×C3C2×D24semidirect
527. C22×C3D3×D8semidirect
548. C2×D3C2×D24semidirect
569. C32C2×#466semidirect
609. C8D3×#67semidirect
630. D3#5115direct (N × H)
647. C22D3×D24semidirect
657. C3D3×#466semidirect
658. C3C2×#5115semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×C3×D3×C82
D3×#9302
C2×D3×D242
#105928142
C3×#51152
#105911642
D3×#8212
#105908322
#105908312
#105908262
D3×#8182
C2×#51153
D3×#4663