Subgroups — #27136121

Order 12352.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#13095400	C₂	1	2	yes	maximal
2	C₈×Dic₁₉₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#13095400	—	2	2	no	—
4	C₂×#13095393	C₄	1	1	yes	characteristic
5	C₄×Dic₁₉₃	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₁₉₃	C₄	1	1	yes	characteristic
7	#13095400	—	4	2	no	—
8	C₂×Dic₁₉₃	D₄	1	1	yes	characteristic
9	C₂×Dic₁₉₃	Q₈	1	1	yes	characteristic
10	#13095393	C₈	1	2	yes	complemented
11	C₂×C₄×C₁₉₃	C₂×C₄	1	1	yes	characteristic
12	C₈×C₁₉₃	—	2	1	no	—
13	C₂²×C₁₉₃	C₄⋊C₄	1	1	yes	characteristic
14	C₄×C₁₉₃	C₂×C₈	1	1	yes	characteristic
15	C₄×C₁₉₃	M₁₆	1	1	yes	characteristic
16	Dic₁₉₃	—	2	1	no	—
17	Dic₁₉₃	SD₁₆	1	2	yes	—
18	C₂×C₁₉₃	C₄⋊C₈	1	1	yes	characteristic
19	C₂×C₁₉₃	#106	1	1	yes	characteristic
20	C₂×C₁₉₃	#108	1	1	yes	characteristic
21	C₁₉₃	#334	1	1	yes	characteristic, complemented, Sylow
22	#334	—	193	1	no	maximal, Sylow
23	C₄⋊C₈	—	193	2	no	—
24	C₄×C₈	—	193	1	no	—
25	C₂×C₈	—	386	2	no	—
26	C₂×C₈	—	193	1	no	—
27	C₂×C₈	#11715871	1	1	yes	characteristic
28	C₄²	—	193	1	no	—
29	C₂×C₄	—	193	1	no	—
30	C₂×C₄	—	193	1	no	—
31	C₂×C₄	C₂×#11715871	1	1	yes	characteristic
32	C₈	—	2	1	no	—
33	C₈	—	772	2	no	—
34	C₈	—	193	2	no	—
35	C₂²	C₄⋊#11715871	1	1	yes	characteristic
36	C₄	—	386	1	no	—
37	C₄	—	193	2	no	—
38	C₄	#15690563	1	1	yes	characteristic
39	C₄	#15690564	1	1	yes	characteristic
40	C₂	#20259966	1	1	yes	characteristic
41	C₂	#20259967	1	1	yes	characteristic
42	C₂	#20259970	1	1	yes	characteristic

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

N	H ≅ G/N	type
10. #13095393	C₈	semidirect
21. C₁₉₃	#334	semidirect

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