Subgroups — #28383358

Order 14272.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20297244	C₂	1	2	yes	maximal
2	#97×C₂₂₃	C₂	1	1	yes	maximal, characteristic
3	C₂₂₃⋊C₁₆	C₄	1	4	yes	complemented
4	C₂×C₈×C₂₂₃	C₄	1	1	yes	characteristic
5	C₂×C₈×C₂₂₃	C₂²	1	1	yes	characteristic
6	C₄²×C₂₂₃	C₄	1	1	yes	characteristic
7	C₂×C₄×C₂₂₃	—	2	1	no	—
8	C₂×C₄×C₂₂₃	C₂×C₄	1	1	yes	characteristic
9	C₈×C₂₂₃	—	2	1	no	—
10	C₈×C₂₂₃	C₂×C₄	1	2	yes	—
11	C₂²×C₂₂₃	M₁₆	1	1	yes	characteristic
12	C₄×C₂₂₃	—	4	1	no	—
13	C₄×C₂₂₃	C₄²	1	1	yes	characteristic
14	C₄×C₂₂₃	M₁₆	1	1	yes	characteristic
15	C₂×C₂₂₃	—	2	1	no	—
16	C₂×C₂₂₃	#97	1	1	yes	characteristic
17	C₂₂₃	#347	1	1	yes	characteristic, complemented, Sylow
18	#347	—	223	1	no	maximal, Sylow
19	M₃₂	—	223	2	no	—
20	#97	D₂₂₃	1	1	yes	characteristic
21	C₂×C₈	Dic₂₂₃	1	1	yes	characteristic
22	C₂×C₈	C₂×D₂₂₃	1	1	yes	characteristic
23	C₄²	Dic₂₂₃	1	1	yes	characteristic
24	C₁₆	—	223	4	no	—
25	C₂×C₄	—	2	1	no	—
26	C₂×C₄	C₂×Dic₂₂₃	1	1	yes	characteristic
27	C₈	—	2	1	no	—
28	C₈	C₄×D₂₂₃	1	2	yes	—
29	C₂²	#16813154	1	1	yes	characteristic
30	C₄	—	4	1	no	—
31	C₄	C₄×Dic₂₂₃	1	1	yes	characteristic
32	C₄	#16813154	1	1	yes	characteristic
33	C₂	—	2	1	no	—
34	C₂	#20297215	1	1	yes	characteristic

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

N	H ≅ G/N	type
3. C₂₂₃⋊C₁₆	C₄	semidirect
17. C₂₂₃	#347	semidirect

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