Finite Group Databasebeta

← #13148062

Subgroups — #13148062

Order 1728.

728 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721724C211yesmaximal, characteristic, complemented
2C3×#63446C211yesmaximal, characteristic
3C9×#879C211yesmaximal, characteristic, complemented
4#611⋊Dic3C211yesmaximal, characteristic, complemented
5#11721269C211yesmaximal, characteristic, complemented
6#11721269C211yesmaximal, characteristic, complemented
7#11721260C211yesmaximal, characteristic, complemented
8#11720996C211yesmaximal, characteristic, complemented
9Dic3×D36C211yesmaximal, characteristic, complemented
10#11720981C211yesmaximal, characteristic, complemented
11D9×Dic3⋊C4C211yesmaximal, characteristic, complemented
12#11720946C211yesmaximal, characteristic, complemented
13#11720945C211yesmaximal, characteristic, complemented
14#11720925C211yesmaximal, characteristic, complemented
15#11720914C211yesmaximal, characteristic, complemented
16#10594113—31nomaximal
17#10589809—31nomaximal
18C22×C3⋊Dic9C2211yescharacteristic
19C2×#6226C2211yescharacteristic
20C2×C3×#611C2211yescharacteristic
21C2×C3×#611C2211yescharacteristic
22C2×C3×D36C2211yescharacteristic
23C2×C3×C4×D9C2211yescharacteristic
24C2×Dic3×D9C2211yescharacteristic
25C2×Dic3×D9C2211yescharacteristic
26C2×Dic3×D9C2211yescharacteristic
27C3×C9×C22⋊C4C2211yescharacteristic
28#88551C2211yescharacteristic
29C4⋊(C3⋊Dic9)C2211yescharacteristic
30#88534C2211yescharacteristic
31#88534C2211yescharacteristic
32C9×#217C2211yescharacteristic
33C9×#217C2211yescharacteristic
34C3×(C2×D9)⋊C4C2211yescharacteristic
35C9×C4⋊Dic3C2211yescharacteristic
36C9×Dic3⋊C4C2211yescharacteristic
37C9×Dic3⋊C4C2211yescharacteristic
38C4×C9×Dic3C2211yescharacteristic
39C3×Dic9⋊C4C2211yescharacteristic
40(C2×D9)⋊Dic3C2211yescharacteristic
41(C2×D9)⋊Dic3C2211yescharacteristic
42(C2×D9)⋊Dic3C2211yescharacteristic
43(C2×D9)⋊Dic3C2211yescharacteristic
44(C2×D9)⋊Dic3C2211yescharacteristic
45Dic3⋊Dic9C2211yescharacteristic
46Dic3⋊Dic9C2211yescharacteristic
47Dic3⋊Dic9C2211yescharacteristic
48Dic3⋊Dic9C2211yescharacteristic
49#88442C2211yescharacteristic
50#88442C2211yescharacteristic
51Dic9⋊Dic3C2211yescharacteristic
52Dic3×Dic9C2211yescharacteristic
53#64087—31no—
54C3×#884—31no—
55C3×#879D311yescharacteristic
56#67⋊Dic3—31no—
57#63969—31no—
58#63969—31no—
59#63962—31no—
60#63896—31no—
61Dic3×D12—31no—
62#63884—31no—
63D3×Dic3⋊C4—31no—
64#63867—31no—
65#63858—31no—
66#63857—31no—
67#63845—31no—
68C9×#126—31no—
69#63460—31no—
70#63459—31no—
71#63458—31no—
72#63456—31no—
73C4⋊C4×D9—31no—
74#63452—31no—
75#63448—31no—
76#63446D311yescharacteristic
77#63445—31no—
78#63445—31no—
79#611⋊C4—31no—
80#63440—31no—
81#63440—61no—
82C4×D36—31no—
83#63432—31no—
84C23×C3×C9C2311yescharacteristic
85C22×C3×D9C2311yescharacteristic
86C22×C3×D9C2311yescharacteristic
87C2×C3×C4×C9C2311yescharacteristic
88C2×C3×C4×C9C2311yescharacteristic
89C2×C3⋊Dic9—41no—
90C2×C3⋊Dic9C2311yescharacteristic
91C2×C3⋊Dic9C2311yescharacteristic
92C2×C3⋊Dic9C2311yescharacteristic
93C2×C3⋊Dic9C2311yescharacteristic
94#6226—41no—
95C3×#611—22no—
96C3×#611—41no—
97C2×C9×Dic3C2311yescharacteristic
98C2×C9×Dic3C2311yescharacteristic
99C2×C9×Dic3C2311yescharacteristic
100C2×C9×Dic3C2311yescharacteristic
101C2×C3×Dic9C2311yescharacteristic
102C2×C3×Dic9C2311yescharacteristic
103C3×D36—22no—
104C3×C4×D9—41no—
105Dic3×D9—22no—
106Dic3×D9—41no—
107Dic3×D9—41no—
108#5707—91no—
109#5602—91no—
110C22×C3⋊Dic3—31no—
111C2×#634—31no—
112C2×C3×#67—31no—
113C2×C3×#67—31no—
114C2×C3×D12—31no—
115C2×C3×C4×D3—31no—
116C2×D3×Dic3—31no—
117C2×D3×Dic3—31no—
118C2×D3×Dic3—31no—
119C32×C22⋊C4C2×D311yescharacteristic
120#3757—31no—
121C4⋊(C3⋊Dic3)—31no—
122#3750—31no—
123#3750—31no—
124C3×#217C2×D311yescharacteristic
125C3×#217C2×D311yescharacteristic
126C3×(C2×D3)⋊C4—31no—
127C3×C4⋊Dic3C2×D311yescharacteristic
128C3×Dic3⋊C4—31no—
129C3×Dic3⋊C4C2×D311yescharacteristic
130C3×Dic3⋊C4C2×D311yescharacteristic
131C3×C4×Dic3C2×D311yescharacteristic
132#3724—31no—
133#3724—31no—
134Dic3⋊Dic3—31no—
135Dic3⋊Dic3—31no—
136Dic3⋊Dic3—31no—
137Dic3⋊Dic3—31no—
138Dic3⋊Dic3—31no—
139(C2×D3)⋊Dic3—31no—
140(C2×D3)⋊Dic3—31no—
141(C2×D3)⋊Dic3—31no—
142(C2×D3)⋊Dic3—31no—
143(C2×D3)⋊Dic3—31no—
144Dic32—31no—
145C2×#611C2×D311yescharacteristic
146C2×#611C2×D311yescharacteristic
147C22×Dic9—31no—
148C22×Dic9—61no—
149C2×D36C2×D311yescharacteristic
150C2×C4×D9—31no—
151C2×C4×D9—31no—
152C2×C4×D9—31no—
153C2×C4×D9C2×D311yescharacteristic
154C2×Dic18—31no—
155C2×Dic18—61no—
156C9×C4⋊C4—31no—
157C9×C4⋊C4—31no—
158C9×C4⋊C4—31no—
159C9×C22⋊C4—21no—
160C9×C22⋊C4—31no—
161C9×C22⋊C4—31no—
162C9×C22⋊C4C2×D311yescharacteristic
163C42×C9—31no—
164#3676—31no—
165#3676—61no—
166(C2×D9)⋊C4—31no—
167(C2×D9)⋊C4—31no—
168(C2×D9)⋊C4—31no—
169(C2×D9)⋊C4—31no—
170(C2×D9)⋊C4—31no—
171(C2×D9)⋊C4C2×D311yescharacteristic
172C4⋊Dic9—31no—
173C4⋊Dic9—31no—
174C4⋊Dic9—31no—
175C4⋊Dic9—31no—
176C4⋊Dic9—31no—
177C4⋊Dic9—61no—
178Dic9⋊C4—31no—
179Dic9⋊C4—31no—
180Dic9⋊C4—31no—
181Dic9⋊C4—31no—
182Dic9⋊C4—31no—
183Dic9⋊C4—61no—
184Dic9⋊C4—61no—
185Dic9⋊C4C2×D311yescharacteristic
186C4×Dic9—31no—
187C22×C3×C9—21no—
188C22×C3×C9—21no—
189C22×C3×C9—21no—
190C22×C3×C9C2411yescharacteristic
191C2×C3×D9—21no—
192C2×C3×D9—21no—
193C2×C3×D9—21no—
194C2×C3×D9—21no—
195C2×C3×D9—21no—
196C2×C3×D9#4112yes—
197C3×C4×C9—21no—
198C3×C4×C9—21no—
199C3⋊Dic9—21no—
200C3⋊Dic9—21no—
201C3⋊Dic9—21no—
202C3⋊Dic9—21no—
203C9×Dic3—21no—
204C9×Dic3—21no—
205C9×Dic3—21no—
206C9×Dic3—21no—
207C3×Dic9—21no—
208C3×Dic9—21no—
209C3×#126—31no—
210C3×#121—91no—
211#935—91no—
212#935—91no—
213#935—91no—
214#935—91no—
215D4×Dic3—91no—
216D4×Dic3—91no—
217#924—91no—
218C2×Dic3⋊C4—91no—
219#898—91no—
220#897—91no—
221#896—91no—
222#894—91no—
223D3×C4⋊C4—91no—
224#890—91no—
225#889—91no—
226#889—91no—
227#886—91no—
228#884—31no—
229#883—91no—
230#883—91no—
231#67⋊C4—91no—
232#879—91no—
233#879D911yescharacteristic, complemented
234#878—91no—
235#878—91no—
236#878—91no—
237#878—181no—
238C4×D12—91no—
239#870—91no—
240C23×C32C22×D311yescharacteristic
241C22×C3×D3—31no—
242C22×C3×D3—31no—
243C2×C32×C4C22×D311yescharacteristic
244C2×C32×C4C22×D311yescharacteristic
245C2×C3⋊Dic3—31no—
246C2×C3⋊Dic3—31no—
247C2×C3⋊Dic3—31no—
248C2×C3⋊Dic3—31no—
249C2×C3⋊Dic3—121no—
250#634—121no—
251C3×#67—62no—
252C3×#67—121no—
253C2×C3×Dic3—31no—
254C2×C3×Dic3—31no—
255C2×C3×Dic3C22×D311yescharacteristic
256C2×C3×Dic3C22×D311yescharacteristic
257C2×C3×Dic3C22×D311yescharacteristic
258C2×C3×Dic3C22×D311yescharacteristic
259C3×D12—62no—
260C3×C4×D3—121no—
261D3×Dic3—62no—
262D3×Dic3—121no—
263D3×Dic3—121no—
264C23×C9—21no—
265C23×C9C22×D311yescharacteristic
266C22×D9C22×D311yescharacteristic
267C22×D9C22×D311yescharacteristic
268C2×C4×C9—21no—
269C2×C4×C9—21no—
270C2×C4×C9—31no—
271C2×C4×C9—31no—
272C2×C4×C9—31no—
273C2×C4×C9—31no—
274C2×C4×C9C22×D311yescharacteristic
275C2×C4×C9C22×D311yescharacteristic
276#611—22no—
277#611—41no—
278C2×Dic9—31no—
279C2×Dic9—31no—
280C2×Dic9—31no—
281C2×Dic9—31no—
282C2×Dic9—61no—
283C2×Dic9—61no—
284C2×Dic9—61no—
285C2×Dic9—61no—
286C2×Dic9—121no—
287C2×Dic9—122no—
288C2×Dic9C22×D311yescharacteristic
289C2×Dic9C22×D311yescharacteristic
290D36—22no—
291C4×D9—41no—
292C4×D9—62no—
293C4×D9—121no—
294C4×D9—121no—
295Dic18—121no—
296Dic18—122no—
297#539—271noSylow
298C2×C3×C9—41no—
299C2×C3×C9C2×#4111yescharacteristic
300C2×C3×C9H(5,𝔽2)11yescharacteristic
301C2×C3×C92−1+411yescharacteristic
302C3×D9—22no—
303C3×D9—41no—
304C2×C3×D4—91no—
305C2×C3×D4—91no—
306C2×C3×D4—91no—
307C22×C3×C4—91no—
308C2×#67—31no—
309C2×#67—31no—
310C22×Dic3—91no—
311C22×Dic3—91no—
312C22×Dic3—91no—
313C22×Dic3—91no—
314C22×Dic3—91no—
315C22×Dic3—181no—
316C2×D12—31no—
317C2×C4×D3—31no—
318C2×C4×D3—91no—
319C2×C4×D3—91no—
320C2×C4×D3—91no—
321C2×Dic6—91no—
322C2×Dic6—91no—
323C2×Dic6—181no—
324C3×C4⋊C4—31no—
325C3×C4⋊C4—31no—
326C3×C4⋊C4—31no—
327C3×C4⋊C4—91no—
328C3×C22⋊C4—21no—
329C3×C22⋊C4—31no—
330C3×C22⋊C4—31no—
331C3×C22⋊C4—91no—
332C3×C22⋊C4C2×D911yescharacteristic
333C3×C22⋊C4D3211yescharacteristic
334C3×C42—31no—
335#217—91no—
336#217—91no—
337#217—91no—
338#217—91no—
339#217—91no—
340#217—91no—
341#217—91no—
342#217—181no—
343#217C2×D911yescharacteristic
344#217C2×D911yescharacteristic
345(C2×D3)⋊C4—31no—
346(C2×D3)⋊C4—91no—
347(C2×D3)⋊C4—91no—
348(C2×D3)⋊C4—91no—
349(C2×D3)⋊C4—91no—
350(C2×D3)⋊C4—91no—
351C4⋊Dic3—91no—
352C4⋊Dic3—91no—
353C4⋊Dic3—91no—
354C4⋊Dic3—91no—
355C4⋊Dic3—91no—
356C4⋊Dic3—91no—
357C4⋊Dic3—91no—
358C4⋊Dic3—181no—
359C4⋊Dic3C2×D911yescharacteristic
360Dic3⋊C4—31no—
361Dic3⋊C4—91no—
362Dic3⋊C4—91no—
363Dic3⋊C4—91no—
364Dic3⋊C4—91no—
365Dic3⋊C4—91no—
366Dic3⋊C4—91no—
367Dic3⋊C4—91no—
368Dic3⋊C4—91no—
369Dic3⋊C4—91no—
370Dic3⋊C4—91no—
371Dic3⋊C4—91no—
372Dic3⋊C4—91no—
373Dic3⋊C4—91no—
374Dic3⋊C4—181no—
375Dic3⋊C4—181no—
376Dic3⋊C4C2×D911yescharacteristic
377Dic3⋊C4C2×D911yescharacteristic
378C4×Dic3—91no—
379C4×Dic3—91no—
380C4×Dic3C2×D911yescharacteristic
381C22×C32—21no—
382C22×C32—21no—
383C22×C32—21no—
384C22×C32C23×D311yescharacteristic
385C2×C3×D3—32no—
386C2×C3×D3—61no—
387C2×C3×D3—61no—
388C2×C3×D3—61no—
389C2×C3×D3—61no—
390C2×C3×D3—61no—
391C32×C4—21no—
392C32×C4—21no—
393C3⋊Dic3—61no—
394C3⋊Dic3—61no—
395C3⋊Dic3—61no—
396C3⋊Dic3—61no—
397C3×Dic3—21no—
398C3×Dic3—21no—
399C3×Dic3—21no—
400C3×Dic3—21no—
401C3×Dic3—61no—
402C3×Dic3—61no—
403C22×C9—22no—
404C22×C9—21no—
405C22×C9—21no—
406C22×C9—21no—
407C22×C9—21no—
408C22×C9—41no—
409C22×C9—41no—
410C22×C9C23×D311yescharacteristic
411C2×D9—21no—
412C2×D9—21no—
413C2×D9—21no—
414C2×D9—21no—
415C2×D9—21no—
416C2×D9#23712yes—
417C4×C9—21no—
418C4×C9—21no—
419C4×C9—41no—
420C4×C9—41no—
421C4×C9—61no—
422C4×C9—61no—
423C4×C9—61no—
424C4×C9—61no—
425Dic9—21no—
426Dic9—21no—
427Dic9—62no—
428Dic9—61no—
429Dic9—61no—
430Dic9—61no—
431Dic9—61no—
432Dic9—121no—
433Dic9—121no—
434Dic9—121no—
435#126—31no—
436#126—271no—
437#125—271no—
438#125—271no—
439#123—271no—
440#123—271no—
441#123—271no—
442#123—271no—
443C22⋊Q8—271no—
444C22⋊Q8—271no—
445C22⋊Q8—271no—
446#121—91no—
447C4×D4—271no—
448C4×D4—271no—
449C2×C4⋊C4—271no—
450C3×C9#53911yescharacteristic, complemented, Sylow
451C23×C3—21no—
452C23×C3—91no—
453C23×C3—91no—
454C23×C3C22×D911yescharacteristic
455C23×C3C2×D3211yescharacteristic
456C22×D3—31no—
457C22×D3—31no—
458C3×D4—182no—
459C3×D4—182no—
460C3×D4—361no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—31no—
464C2×C3×C4—31no—
465C2×C3×C4—31no—
466C2×C3×C4—31no—
467C2×C3×C4—91no—
468C2×C3×C4—91no—
469C2×C3×C4—361no—
470C2×C3×C4C22×D911yescharacteristic
471C2×C3×C4C22×D911yescharacteristic
472C2×C3×C4C2×D3211yescharacteristic
473C2×C3×C4C2×D3211yescharacteristic
474#67—62no—
475#67—121no—
476C2×Dic3—31no—
477C2×Dic3—31no—
478C2×Dic3—91no—
479C2×Dic3—91no—
480C2×Dic3—91no—
481C2×Dic3—91no—
482C2×Dic3—91no—
483C2×Dic3—91no—
484C2×Dic3—91no—
485C2×Dic3—91no—
486C2×Dic3—181no—
487C2×Dic3—181no—
488C2×Dic3—181no—
489C2×Dic3—181no—
490C2×Dic3—182no—
491C2×Dic3—361no—
492C2×Dic3—361no—
493C2×Dic3—361no—
494C2×Dic3—361no—
495C2×Dic3—362no—
496C2×Dic3C22×D911yescharacteristic
497C2×Dic3C22×D911yescharacteristic
498C2×Dic3C22×D911yescharacteristic
499C2×Dic3C22×D911yescharacteristic
500D12—62no—
501C4×D3—121no—
502C4×D3—182no—
503C4×D3—361no—
504C4×D3—361no—
505Dic6—361no—
506Dic6—361no—
507Dic6—362no—
508C2×C32—41no—
509C2×C32D3×#4111yescharacteristic
510C2×C32#100911yescharacteristic
511C2×C32#101011yescharacteristic
512C3×D3—62no—
513C3×D3—121no—
514C2×C9—21no—
515C2×C9—21no—
516C2×C9—21no—
517C2×C9—42no—
518C2×C9—41no—
519C2×C9C2×#23711yescharacteristic
520C2×C9#100411yescharacteristic
521C2×C9#101011yescharacteristic
522D9—22no—
523D9—41no—
524C2×Q8—271no—
525C2×D4—91no—
526C2×D4—91no—
527C2×D4—91no—
528C22×C4—91no—
529C22×C4—271no—
530C22×C4—271no—
531C22×C4—271no—
532C22×C4—271no—
533C4⋊C4—31no—
534C4⋊C4—31no—
535C4⋊C4—31no—
536C4⋊C4—91no—
537C4⋊C4—271no—
538C4⋊C4—271no—
539C4⋊C4—271no—
540C4⋊C4—271no—
541C4⋊C4—271no—
542C4⋊C4—271no—
543C4⋊C4—271no—
544C4⋊C4—271no—
545C4⋊C4—271no—
546C4⋊C4—271no—
547C22⋊C4—31no—
548C22⋊C4—31no—
549C22⋊C4—91no—
550C22⋊C4—271no—
551C22⋊C4—271no—
552C22⋊C4—271no—
553C22⋊C4—271no—
554C22⋊C4—271no—
555C22⋊C4—271no—
556C22⋊C4D3×D911yescharacteristic
557C42—31no—
558C42—271no—
559C22×C3—22no—
560C22×C3—21no—
561C22×C3—21no—
562C22×C3—21no—
563C22×C3—21no—
564C22×C3—21no—
565C22×C3—21no—
566C22×C3—21no—
567C22×C3—41no—
568C22×C3—41no—
569C22×C3—92no—
570C22×C3—181no—
571C22×C3—181no—
572C22×C3—181no—
573C22×C3—181no—
574C22×C3—181no—
575C22×C3C23×D911yescharacteristic
576C22×C3C22×D3211yescharacteristic
577C2×D3—32no—
578C2×D3—61no—
579C2×D3—61no—
580C2×D3—61no—
581C2×D3—61no—
582C2×D3—61no—
583C3×C4—21no—
584C3×C4—21no—
585C3×C4—21no—
586C3×C4—21no—
587C3×C4—41no—
588C3×C4—41no—
589C3×C4—61no—
590C3×C4—61no—
591C3×C4—61no—
592C3×C4—61no—
593C3×C4—181no—
594C3×C4—181no—
595Dic3—21no—
596Dic3—21no—
597Dic3—21no—
598Dic3—21no—
599Dic3—61no—
600Dic3—61no—
601Dic3—182no—
602Dic3—181no—
603Dic3—181no—
604Dic3—181no—
605Dic3—181no—
606Dic3—181no—
607Dic3—181no—
608Dic3—181no—
609Dic3—181no—
610Dic3—361no—
611Dic3—361no—
612Dic3—361no—
613C32#570711yescharacteristic
614C9—21no—
615C9#560211yescharacteristic, complemented
616C23—91no—
617C23—91no—
618C23C2×D3×D911yescharacteristic
619Q8—1081no—
620D4—182no—
621D4—182no—
622D4—361no—
623C2×C4—31no—
624C2×C4—31no—
625C2×C4—31no—
626C2×C4—31no—
627C2×C4—91no—
628C2×C4—91no—
629C2×C4—271no—
630C2×C4—271no—
631C2×C4—271no—
632C2×C4—271no—
633C2×C4—361no—
634C2×C4—542no—
635C2×C4—1081no—
636C2×C4—1081no—
637C2×C4—1081no—
638C2×C4C2×D3×D911yescharacteristic
639C2×C4C2×D3×D911yescharacteristic
640C2×C3—21no—
641C2×C3—21no—
642C2×C3—21no—
643C2×C3—42no—
644C2×C3—41no—
645C2×C3—41no—
646C2×C3—182no—
647C2×C3—361no—
648C2×C3#41×D911yescharacteristic
649C2×C3#6371511yescharacteristic
650C2×C3#6371611yescharacteristic
651C2×C3#6429811yescharacteristic
652C2×C3D3×#23711yescharacteristic
653C2×C3#6431411yescharacteristic
654D3—62no—
655D3—121no—
656C22—21no—
657C22—21no—
658C22—21no—
659C22—92no—
660C22—181no—
661C22—181no—
662C22—181no—
663C22—181no—
664C22—181no—
665C22C22×D3×D911yescharacteristic
666C4—21no—
667C4—21no—
668C4—61no—
669C4—61no—
670C4—61no—
671C4—61no—
672C4—181no—
673C4—181no—
674C4—541no—
675C4—541no—
676C4—541no—
677C4—541no—
678C3—21no—
679C3#1058980911yescharacteristic, complemented
680C3#1059411311yescharacteristic
681C2—41no—
682C2—182no—
683C2—361no—
684C2#1172246511yescharacteristic
685C2D9×#23711yescharacteristic
686C2#1172250111yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C22⋊C4C22
socleC22×C32C23×D3
prime radicalC3×#63446C2
hypercenterC22⋊C4D3×D9
hypocenterC3×C9#539
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #11721724C2semidirect
3. C9×#879C2semidirect
4. #611⋊Dic3C2semidirect
5. #11721269C2semidirect
6. #11721269C2semidirect
7. #11721260C2semidirect
8. #11720996C2semidirect
9. Dic3×D36C2semidirect
10. #11720981C2semidirect
11. D9×Dic3⋊C4C2semidirect
12. #11720946C2semidirect
13. #11720945C2semidirect
14. #11720925C2semidirect
15. #11720914C2semidirect
233. #879D9semidirect
450. C3×C9#539semidirect
615. C9#5602semidirect
679. C3#10589809semidirect

Maximal subgroups

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

subgroupindex
#117217242
C3×#634462
C9×#8792
#611⋊Dic32
#117212692
#117212602
#117209962
Dic3×D362
#117209812
D9×Dic3⋊C42
#117209462
#117209452
#117209252
#117209142
#105941133
#105898093