Finite Group Databasebeta

← C2×#11722891 #13170688

Subgroups — C2×#11722891 #13170688

Order 1728.

1250 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89040C211yesmaximal, characteristic, complemented
2C2×C3×#3796C211yesmaximal, characteristic
3C2×#88798C211yesmaximal, characteristic, complemented
4C2×#88792C211yesmaximal, characteristic, complemented
5C2×#88787C211yesmaximal, characteristic, complemented
6C2×C3×#3719C211yesmaximal, characteristic, complemented
7C2×C3×#3716C211yesmaximal, characteristic, complemented
8#11722891C218yesmaximal, direct product factor
9C2×#63943—31nomaximal
10C2×#63929—31nomaximal
11C2×#63811—31nomaximal
12C2×C3×C4×C3⋊D3C2211yescharacteristic
13C2×C3×#634C2211yescharacteristic
14C2×C3×#634C2211yescharacteristic
15C2×C32×D12C2211yescharacteristic
16C2×C32×Dic6C2211yescharacteristic
17C2×#6296—21no—
18C2×#6294—21no—
19#89040—22no—
20#89040C2214yescomplemented
21C2×C3×#626—21no—
22C2×C3×D3×Dic3—21no—
23C3×#3796—22no—
24C3×#3796C2214yes—
25C2×C3⋊(C3⋊(C3⋊C8))C2211yescharacteristic
26C2×C32×C3⋊C8C2211yescharacteristic
27#88798C2214yescomplemented
28#88792C2214yescomplemented
29#88787C2214yescomplemented
30C3×#3719C2214yescomplemented
31C3×#3716C2214yescomplemented
32C2×C3×#239—31no—
33C2×C3×#237—31no—
34C2×#3797—31no—
35C2×#3796D311yescharacteristic
36C2×D3×Dic6—31no—
37C2×D3×Dic6—31no—
38C2×#3756—31no—
39C2×#3754—31no—
40C2×#3743—31no—
41C2×C3×#216—31no—
42C2×C3×#214—31no—
43C2×C3×Dic12—31no—
44C2×C3×#204—31no—
45#63943—38no—
46#63929—38no—
47C2×#3719D311yescharacteristic, complemented
48C2×#3718—31no—
49C2×#3718—31no—
50C2×#3718—61no—
51C2×#3716D311yescharacteristic, complemented
52C2×#3715—31no—
53C2×#3715—31no—
54C2×#3715—61no—
55C2×#3711—31no—
56C2×#3711—31no—
57C2×#3711—61no—
58#63811—38no—
59C22×C3×C3⋊D3D411yescharacteristic
60C22×C32×D3—21no—
61C2×C33×C4C2311yescharacteristic
62C2×C3×C3⋊Dic3—21no—
63C2×C3×C3⋊Dic3—21no—
64C2×C3×C3⋊Dic3D411yescharacteristic
65C3×C4×C3⋊D3D412yes—
66C3×C4×C3⋊D3C2312yes—
67C3×#634—21no—
68C3×#634—21no—
69C3×#634C2312yes—
70C3×#634C2312yes—
71C2×C32×Dic3—21no—
72C32×D12—21no—
73C32×D12C2312yes—
74C32×Dic6—21no—
75C32×Dic6C2312yes—
76#6296—24no—
77#6294—24no—
78C3×#626—24no—
79C3×D3×Dic3—24no—
80C3⋊(C3⋊(C3⋊C8))C2312yes—
81C32×C3⋊C8C2312yes—
82C2×#951—91no—
83C2×#918—91no—
84C2×#915—91no—
85C2×C32×Q8—31no—
86C2×C32×D4—31no—
87C2×C4×C3⋊D3C2×D311yescharacteristic
88C2×#634C2×D311yescharacteristic
89C2×#634C2×D311yescharacteristic
90C2×C3×#67—61no—
91C22×C3×Dic3—61no—
92C3×#239—34no—
93C3×#239—62no—
94C3×#237—34no—
95C3×#237—62no—
96C2×C3×D12—21no—
97C2×C3×D12—61no—
98C2×C3×D12C2×D311yescharacteristic
99C2×C3×D12C2×D311yescharacteristic
100C2×C3×C4×D3—31no—
101C2×C3×C4×D3—31no—
102C2×C3×C4×D3—61no—
103C2×C3×C4×D3—61no—
104C2×C3×Dic6—21no—
105C2×C3×Dic6—31no—
106C2×C3×Dic6—31no—
107C2×C3×Dic6—31no—
108C2×C3×Dic6—31no—
109C2×C3×Dic6—61no—
110C2×C3×Dic6—61no—
111C2×C3×Dic6C2×D311yescharacteristic
112C2×C3×Dic6C2×D311yescharacteristic
113C2×#627—61no—
114C2×#627—61no—
115C2×#627—61no—
116C2×#626—21no—
117C2×#624—61no—
118C2×D3×Dic3—21no—
119C2×D3×Dic3—61no—
120C2×D3×Dic3—61no—
121#3797—34no—
122#3797—62no—
123#3796—22no—
124#3796C2×D314yes—
125D3×Dic6—34no—
126D3×Dic6—34no—
127D3×Dic6—62no—
128D3×Dic6—62no—
129C2×C32×C8—31no—
130#3756—34no—
131#3754—34no—
132C2×C3⋊(C3⋊C8)—31no—
133C2×C3⋊(C3⋊C8)—31no—
134C2×C3⋊(C3⋊C8)—31no—
135C2×C3⋊(C3⋊C8)—61no—
136C2×C3⋊(C3⋊C8)—61no—
137C2×C3⋊(C3⋊C8)—61no—
138C2×C3⋊(C3⋊C8)—121no—
139#3743—34no—
140C3×#216—34no—
141C3×#214—34no—
142C2×C3×C3⋊C8—21no—
143C2×C3×C3⋊C8C2×D311yescharacteristic
144C2×C3×C3⋊C8C2×D311yescharacteristic
145C3×Dic12—34no—
146C3×#204—34no—
147#3719C2×D314yescomplemented
148#3718—34no—
149#3718—34no—
150#3718—64no—
151#3716C2×D314yescomplemented
152#3715—34no—
153#3715—34no—
154#3715—64no—
155#3711—34no—
156#3711—34no—
157#3711—64no—
158C22×C33C2×D411yescharacteristic
159C2×C3×C3⋊D3—22no—
160C2×C3×C3⋊D3C2×D412yes—
161C2×C32×D3—22no—
162C2×C32×D3—42no—
163C33×C4C2×D411yescharacteristic
164C33×C4C2411yescharacteristic
165C3×C3⋊Dic3—22no—
166C3×C3⋊Dic3—22no—
167C3×C3⋊Dic3C2×D412yes—
168C32×Dic3—22no—
169C2×C3×#41—91no—
170C2×#239—31no—
171C2×D3×Q8—91no—
172C2×D3×Q8—91no—
173C2×#237—31no—
174C22×Dic6—91no—
175C2×C3×Q16—91no—
176C2×C3×SD16—91no—
177#951—98no—
178C2×#216—31no—
179C2×#216—91no—
180C2×#216—91no—
181C2×#216—91no—
182C2×#216—181no—
183C2×#215—91no—
184C2×#214—31no—
185C2×#214—91no—
186C2×#214—91no—
187C2×#214—181no—
188C2×#208—91no—
189#918—98no—
190#915—98no—
191C2×Dic12—31no—
192C2×#204—31no—
193C2×ΓL(1,𝔽25)—91no—
194C2×ΓL(1,𝔽25)—91no—
195C2×ΓL(1,𝔽25)—181no—
196C23×C32—61no—
197C22×C3⋊D3#6711yescharacteristic
198C22×C3×D3—21no—
199C22×C3×D3—21no—
200C22×C3×D3—31no—
201C22×C3×D3—31no—
202C22×C3×D3—41no—
203C22×C3×D3—61no—
204C32×Q8—32no—
205C32×Q8—61no—
206C32×D4—32no—
207C32×D4—61no—
208C2×C32×C4—21no—
209C2×C32×C4—21no—
210C2×C32×C4—21no—
211C2×C32×C4—41no—
212C2×C32×C4—61no—
213C2×C32×C4C22×D311yescharacteristic
214C2×C32×C4C22×D311yescharacteristic
215C2×C32×C4C22×D311yescharacteristic
216C2×C3⋊Dic3—21no—
217C2×C3⋊Dic3—21no—
218C2×C3⋊Dic3#6711yescharacteristic
219C4×C3⋊D3#6712yes—
220C4×C3⋊D3C22×D312yes—
221#634—21no—
222#634—21no—
223#634C22×D312yes—
224#634C22×D312yes—
225C3×#67—64no—
226C2×C3×Dic3—21no—
227C2×C3×Dic3—21no—
228C2×C3×Dic3—31no—
229C2×C3×Dic3—31no—
230C2×C3×Dic3—41no—
231C2×C3×Dic3—61no—
232C2×C3×Dic3—64no—
233C2×C3×Dic3—61no—
234C2×C3×Dic3—61no—
235C2×C3×Dic3—61no—
236C2×C3×Dic3—61no—
237C2×C3×Dic3—121no—
238C2×C3×Dic3—121no—
239C3×D12—21no—
240C3×D12—21no—
241C3×D12—22no—
242C3×D12—41no—
243C3×D12—64no—
244C3×D12C22×D312yes—
245C3×D12C22×D312yes—
246C3×C4×D3—32no—
247C3×C4×D3—32no—
248C3×C4×D3—32no—
249C3×C4×D3—32no—
250C3×C4×D3—62no—
251C3×C4×D3—62no—
252C3×C4×D3—64no—
253C3×Dic6—21no—
254C3×Dic6—21no—
255C3×Dic6—22no—
256C3×Dic6—32no—
257C3×Dic6—32no—
258C3×Dic6—32no—
259C3×Dic6—32no—
260C3×Dic6—41no—
261C3×Dic6—62no—
262C3×Dic6—62no—
263C3×Dic6—61no—
264C3×Dic6—61no—
265C3×Dic6—61no—
266C3×Dic6—61no—
267C3×Dic6—121no—
268C3×Dic6—121no—
269C3×Dic6C22×D312yes—
270C3×Dic6C22×D312yes—
271#627—64no—
272#627—64no—
273#627—64no—
274#626—24no—
275#624—64no—
276D3×Dic3—24no—
277D3×Dic3—64no—
278D3×Dic3—64no—
279C32×C8—32no—
280C3⋊(C3⋊C8)—32no—
281C3⋊(C3⋊C8)—32no—
282C3⋊(C3⋊C8)—32no—
283C3⋊(C3⋊C8)—62no—
284C3⋊(C3⋊C8)—62no—
285C3⋊(C3⋊C8)—62no—
286C3⋊(C3⋊C8)—122no—
287C3×C3⋊C8—22no—
288C3×C3⋊C8C22×D312yes—
289C3×C3⋊C8C22×D312yes—
290C2×#137—271noSylow
291C2×C33#13712yescomplemented
292C2×C33C22×D411yescharacteristic
293C3×C3⋊D3—22no—
294C32×D3—42no—
295C3×#41—94no—
296C3×#41—182no—
297C2×C3×Q8—31no—
298C2×C3×Q8—31no—
299C2×C3×Q8—61no—
300C2×C3×Q8—91no—
301C2×C3×Q8—91no—
302C2×C3×D4—31no—
303C2×C3×D4—31no—
304C2×C3×D4—61no—
305C2×C3×D4—181no—
306C22×C3×C4—91no—
307C22×C3×C4—181no—
308C2×#67—61no—
309C22×Dic3—61no—
310C22×Dic3—181no—
311#239—34no—
312#239—62no—
313D3×Q8—94no—
314D3×Q8—94no—
315D3×Q8—182no—
316D3×Q8—182no—
317#237—34no—
318#237—62no—
319C2×D12—61no—
320C2×D12D3211yescharacteristic
321C2×C4×D3—31no—
322C2×C4×D3—31no—
323C2×C4×D3—61no—
324C2×C4×D3—61no—
325C2×C4×D3—181no—
326C2×C4×D3—181no—
327C2×Dic6—31no—
328C2×Dic6—31no—
329C2×Dic6—31no—
330C2×Dic6—31no—
331C2×Dic6—61no—
332C2×Dic6—61no—
333C2×Dic6—94no—
334C2×Dic6—182no—
335C2×Dic6—181no—
336C2×Dic6—181no—
337C2×Dic6—181no—
338C2×Dic6D3211yescharacteristic
339C3×Q16—94no—
340C3×SD16—94no—
341C2×C3×C8—31no—
342C2×C3×C8—31no—
343C2×C3×C8—61no—
344#216—34no—
345#216—94no—
346#216—94no—
347#216—94no—
348#216—184no—
349#215—94no—
350#214—34no—
351#214—94no—
352#214—94no—
353#214—184no—
354#208—94no—
355C2×C3⋊C8—91no—
356C2×C3⋊C8—91no—
357C2×C3⋊C8—91no—
358C2×C3⋊C8—181no—
359C2×C3⋊C8—181no—
360C2×C3⋊C8—181no—
361C2×C3⋊C8—361no—
362C2×C3⋊C8D3211yescharacteristic
363Dic12—34no—
364#204—34no—
365ΓL(1,𝔽25)—94no—
366ΓL(1,𝔽25)—94no—
367ΓL(1,𝔽25)—184no—
368C22×C32—21no—
369C22×C32—21no—
370C22×C32—21no—
371C22×C32—41no—
372C22×C32—62no—
373C22×C32—122no—
374C22×C32D3×D411yescharacteristic
375C22×C32D3×D411yescharacteristic
376C22×C32C2×#6711yescharacteristic
377C2×C3⋊D3—22no—
378C2×C3⋊D3C2×#6712yes—
379C2×C3×D3—22no—
380C2×C3×D3—22no—
381C2×C3×D3—32no—
382C2×C3×D3—32no—
383C2×C3×D3—42no—
384C2×C3×D3—42no—
385C2×C3×D3—42no—
386C2×C3×D3—62no—
387C2×C3×D3—62no—
388C2×C3×D3—62no—
389C2×C3×D3—82no—
390C2×C3×D3—122no—
391C32×C4—21no—
392C32×C4—21no—
393C32×C4—21no—
394C32×C4—21no—
395C32×C4—21no—
396C32×C4—21no—
397C32×C4—41no—
398C32×C4—41no—
399C32×C4—62no—
400C32×C4D3×D411yescharacteristic
401C32×C4D3×D411yescharacteristic
402C32×C4C2×#6711yescharacteristic
403C32×C4C23×D311yescharacteristic
404C32×C4C23×D311yescharacteristic
405C32×C4C23×D311yescharacteristic
406C3⋊Dic3—22no—
407C3⋊Dic3—22no—
408C3⋊Dic3C2×#6712yes—
409C3×Dic3—22no—
410C3×Dic3—22no—
411C3×Dic3—32no—
412C3×Dic3—32no—
413C3×Dic3—42no—
414C3×Dic3—62no—
415C3×Dic3—62no—
416C3×Dic3—62no—
417C3×Dic3—62no—
418C3×Dic3—62no—
419C3×Dic3—122no—
420C3×Dic3—122no—
421C2×#41—91no—
422C22×Q8—271no—
423#137—278no—
424C2×Q16—91no—
425C2×Q16—271no—
426C2×SD16—91no—
427C2×SD16—271no—
428C2×M16—271no—
429C33C2×#13711yescharacteristic, complemented, Sylow
430C23×C3—61no—
431C23×C3—61no—
432C23×C3—91no—
433C23×C3—121no—
434C22×D3—21no—
435C22×D3—31no—
436C22×D3—31no—
437C22×D3—61no—
438C3×Q8—32no—
439C3×Q8—32no—
440C3×Q8—62no—
441C3×Q8—61no—
442C3×Q8—61no—
443C3×Q8—92no—
444C3×Q8—92no—
445C3×Q8—121no—
446C3×Q8—181no—
447C3×Q8—181no—
448C3×D4—32no—
449C3×D4—32no—
450C3×D4—62no—
451C3×D4—61no—
452C3×D4—61no—
453C3×D4—121no—
454C3×D4—184no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—41no—
459C2×C3×C4—61no—
460C2×C3×C4—61no—
461C2×C3×C4—91no—
462C2×C3×C4—92no—
463C2×C3×C4—92no—
464C2×C3×C4—121no—
465C2×C3×C4—184no—
466C2×C3×C4—181no—
467C2×C3×C4—181no—
468C2×C3×C4C2×D3211yescharacteristic
469C2×C3×C4C2×D3211yescharacteristic
470C2×C3×C4C2×D3211yescharacteristic
471#67—64no—
472C2×Dic3—21no—
473C2×Dic3—31no—
474C2×Dic3—31no—
475C2×Dic3—61no—
476C2×Dic3—64no—
477C2×Dic3—61no—
478C2×Dic3—61no—
479C2×Dic3—61no—
480C2×Dic3—61no—
481C2×Dic3—121no—
482C2×Dic3—121no—
483C2×Dic3—184no—
484D12—21no—
485D12—64no—
486D12C2×D3212yes—
487C4×D3—32no—
488C4×D3—32no—
489C4×D3—32no—
490C4×D3—32no—
491C4×D3—62no—
492C4×D3—62no—
493C4×D3—64no—
494C4×D3—184no—
495C4×D3—184no—
496Dic6—21no—
497Dic6—32no—
498Dic6—32no—
499Dic6—32no—
500Dic6—32no—
501Dic6—62no—
502Dic6—62no—
503Dic6—61no—
504Dic6—61no—
505Dic6—61no—
506Dic6—61no—
507Dic6—121no—
508Dic6—121no—
509Dic6—184no—
510Dic6—184no—
511Dic6—184no—
512Dic6C2×D3212yes—
513C3×C8—32no—
514C3×C8—32no—
515C3×C8—62no—
516C3⋊C8—92no—
517C3⋊C8—92no—
518C3⋊C8—92no—
519C3⋊C8—182no—
520C3⋊C8—182no—
521C3⋊C8—182no—
522C3⋊C8—362no—
523C3⋊C8C2×D3212yes—
524C2×C32—21no—
525C2×C32—22no—
526C2×C32—21no—
527C2×C32—21no—
528C2×C32—22no—
529C2×C32—22no—
530C2×C32—42no—
531C2×C32—41no—
532C2×C32—122no—
533C2×C32#91512yescomplemented
534C2×C32#91812yescomplemented
535C2×C32#95112yescomplemented
536C2×C32C2×D3×D411yescharacteristic
537C2×C32C2×D3×D411yescharacteristic
538C2×C32C22×#6711yescharacteristic
539C3⋊D3—22no—
540C3×D3—42no—
541C3×D3—42no—
542C3×D3—62no—
543C3×D3—62no—
544C3×D3—82no—
545C3×D3—122no—
546#41—94no—
547#41—182no—
548C2×Q8—31no—
549C2×Q8—91no—
550C2×Q8—91no—
551C2×Q8—274no—
552C2×Q8—541no—
553C2×Q8—542no—
554C2×D4—31no—
555C2×D4—181no—
556C22×C4—91no—
557C22×C4—181no—
558C22×C4—541no—
559Q16—94no—
560Q16—274no—
561SD16—94no—
562SD16—274no—
563M16—274no—
564C2×C8—31no—
565C2×C8—271no—
566C22×C3—21no—
567C22×C3—21no—
568C22×C3—21no—
569C22×C3—41no—
570C22×C3—62no—
571C22×C3—62no—
572C22×C3—92no—
573C22×C3—122no—
574C22×C3—122no—
575C22×C3—122no—
576C22×C3—182no—
577C22×C3—242no—
578C22×C3#380211yescharacteristic
579C22×C3D3×#6711yescharacteristic
580C22×C3D3×#6711yescharacteristic
581C2×D3—22no—
582C2×D3—32no—
583C2×D3—32no—
584C2×D3—42no—
585C2×D3—62no—
586C2×D3—62no—
587C2×D3—62no—
588C2×D3—122no—
589C3×C4—21no—
590C3×C4—21no—
591C3×C4—21no—
592C3×C4—21no—
593C3×C4—21no—
594C3×C4—21no—
595C3×C4—41no—
596C3×C4—41no—
597C3×C4—62no—
598C3×C4—62no—
599C3×C4—92no—
600C3×C4—122no—
601C3×C4—182no—
602C3×C4—182no—
603C3×C4#380211yescharacteristic
604C3×C4D3×#6711yescharacteristic
605C3×C4D3×#6711yescharacteristic
606C3×C4C22×D3211yescharacteristic
607C3×C4C22×D3211yescharacteristic
608C3×C4C22×D3211yescharacteristic
609Dic3—22no—
610Dic3—32no—
611Dic3—32no—
612Dic3—62no—
613Dic3—62no—
614Dic3—62no—
615Dic3—62no—
616Dic3—62no—
617Dic3—122no—
618Dic3—122no—
619C32—21no—
620C32—21no—
621C32—21no—
622C32—41no—
623C32C2×#91511yescharacteristic, complemented
624C32C2×#91811yescharacteristic, complemented
625C32C2×#95111yescharacteristic, complemented
626C23—61no—
627C23—91no—
628Q8—32no—
629Q8—61no—
630Q8—92no—
631Q8—92no—
632Q8—181no—
633Q8—181no—
634Q8—544no—
635D4—32no—
636D4—61no—
637D4—184no—
638C2×C4—61no—
639C2×C4—91no—
640C2×C4—92no—
641C2×C4—92no—
642C2×C4—184no—
643C2×C4—181no—
644C2×C4—181no—
645C2×C4—544no—
646C2×C4D3311yescharacteristic
647C8—32no—
648C8—272no—
649C2×C3—21no—
650C2×C3—21no—
651C2×C3—21no—
652C2×C3—22no—
653C2×C3—22no—
654C2×C3—22no—
655C2×C3—41no—
656C2×C3—42no—
657C2×C3—122no—
658C2×C3—122no—
659C2×C3—182no—
660C2×C3—242no—
661C2×C3#6381112yescomplemented
662C2×C3#6392912yescomplemented
663C2×C3#6394312yescomplemented
664C2×C3C2×#380211yescharacteristic
665C2×C3C2×D3×#6711yescharacteristic
666C2×C3C2×D3×#6711yescharacteristic
667D3—42no—
668D3—62no—
669D3—62no—
670D3—122no—
671C22—62no—
672C22—92no—
673C22—122no—
674C22—182no—
675C22#8895311yescharacteristic
676C4—62no—
677C4—92no—
678C4—182no—
679C4—182no—
680C4#8895311yescharacteristic
681C4C2×D3311yescharacteristic
682C3—21no—
683C3—21no—
684C3—21no—
685C3—41no—
686C3C2×#6381111yescharacteristic, complemented
687C3C2×#6392911yescharacteristic, complemented
688C3C2×#6394311yescharacteristic, complemented
689C2—122no—
690C2—182no—
691C2#1172289112yesdirect product factor
692C2C2×#8895311yescharacteristic
subgroupG/H
centerC22#88953
commutator, cosocleC33×C4C24
FrattiniC4C2×D33
FittingC2×C33×C4C23
socleC22×C33C2×D4
prime radicalC2×C3×#3796C2
hypercenterC2×C4D33
hypocenterC33C2×#137
LCSG ▷ C33×C4 ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C2×#89040C2semidirect
3. C2×#88798C2semidirect
4. C2×#88792C2semidirect
5. C2×#88787C2semidirect
6. C2×C3×#3719C2semidirect
7. C2×C3×#3716C2semidirect
8. #11722891C2direct (N × H)
20. #89040C22semidirect
27. #88798C22semidirect
28. #88792C22semidirect
29. #88787C22semidirect
30. C3×#3719C22semidirect
31. C3×#3716C22semidirect
47. C2×#3719D3semidirect
51. C2×#3716D3semidirect
147. #3719C2×D3semidirect
151. #3716C2×D3semidirect
291. C2×C33#137semidirect
429. C33C2×#137semidirect
533. C2×C32#915semidirect
534. C2×C32#918semidirect
535. C2×C32#951semidirect
623. C32C2×#915semidirect
624. C32C2×#918semidirect
625. C32C2×#951semidirect
661. C2×C3#63811semidirect
662. C2×C3#63929semidirect
663. C2×C3#63943semidirect
686. C3C2×#63811semidirect
687. C3C2×#63929semidirect
688. C3C2×#63943semidirect
691. C2#11722891direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#890402
C2×C3×#37962
C2×#887982
C2×#887922
C2×#887872
C2×C3×#37192
C2×C3×#37162
#117228912
C2×#639433
C2×#639293
C2×#638113