Subgroups — #27136147

Order 12352.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15690558	C₂	1	2	yes	maximal
2	C₄×#13095393	C₂	1	1	yes	maximal, characteristic
3	#15690558	C₄	1	4	yes	complemented
4	C₂×#13095393	C₄	1	1	yes	characteristic
5	C₂×#13095393	C₂²	1	1	yes	characteristic
6	C₄²×C₁₉₃	C₄	1	1	yes	characteristic
7	#13095393	C₈	1	2	yes	—
8	#13095393	C₂×C₄	1	2	yes	—
9	C₂×C₄×C₁₉₃	C₈	1	2	yes	—
10	C₂×C₄×C₁₉₃	C₂×C₄	1	1	yes	characteristic
11	C₂²×C₁₉₃	C₂×C₈	1	1	yes	characteristic
12	C₄×C₁₉₃	—	2	2	no	—
13	C₄×C₁₉₃	C₄²	1	1	yes	characteristic
14	C₄×C₁₉₃	C₂×C₈	1	1	yes	characteristic
15	C₂×C₁₉₃	C₄×C₈	1	1	yes	characteristic
16	C₂×C₁₉₃	M₃₂	1	2	yes	—
17	C₁₉₃	#346	1	1	yes	characteristic, complemented, Sylow
18	#346	—	193	1	no	maximal, Sylow
19	C₂×C₁₆	—	193	2	no	—
20	C₄×C₈	—	193	1	no	—
21	C₂×C₈	—	193	1	no	—
22	C₂×C₈	—	193	1	no	—
23	C₄²	#11715871	1	1	yes	characteristic
24	C₁₆	—	193	4	no	—
25	C₂×C₄	#13095400	1	2	yes	—
26	C₂×C₄	C₂×#11715871	1	1	yes	characteristic
27	C₈	—	193	2	no	—
28	C₈	—	193	2	no	—
29	C₂²	C₂×#13095400	1	1	yes	characteristic
30	C₄	—	2	2	no	—
31	C₄	C₄×#11715871	1	1	yes	characteristic
32	C₄	#15690563	1	1	yes	characteristic
33	C₂	C₄×#13095400	1	1	yes	characteristic
34	C₂	#20259973	1	2	yes	—

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

N	H ≅ G/N	type
3. #15690558	C₄	semidirect
17. C₁₉₃	#346	semidirect

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