Subgroups — #28383410

Order 14272.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20297240	C₂	1	2	yes	maximal
2	C₂×C₁₆×C₂₂₃	C₂	1	1	yes	maximal, characteristic
3	#16813154	—	2	2	no	—
4	C₂×C₈×C₂₂₃	C₂²	1	1	yes	characteristic
5	C₁₆×C₂₂₃	C₄	1	2	yes	—
6	C₂₂₃⋊C₈	—	4	2	no	—
7	C₂×C₄×C₂₂₃	D₄	1	1	yes	characteristic
8	C₈×C₂₂₃	C₂×C₄	1	1	yes	characteristic
9	C₈×C₂₂₃	Q₈	1	1	yes	characteristic
10	C₂²×C₂₂₃	Q₁₆	1	1	yes	characteristic
11	C₄×C₂₂₃	C₄⋊C₄	1	1	yes	characteristic
12	C₄×C₂₂₃	D₈	1	1	yes	characteristic
13	C₂×C₂₂₃	—	2	1	no	—
14	C₂×C₂₂₃	#107	1	1	yes	characteristic
15	C₂₂₃	#368	1	1	yes	characteristic, complemented, Sylow
16	#368	—	223	1	no	maximal, Sylow
17	C₂×C₁₆	D₂₂₃	1	1	yes	characteristic
18	#108	—	223	2	no	—
19	M₁₆	—	446	2	no	—
20	C₂×C₈	C₂×D₂₂₃	1	1	yes	characteristic
21	C₁₆	Dic₂₂₃	1	2	yes	—
22	C₂×C₄	D₈₉₂	1	1	yes	characteristic
23	C₈	—	892	2	no	—
24	C₈	C₂×Dic₂₂₃	1	1	yes	characteristic
25	C₈	Dic₄₄₆	1	1	yes	characteristic
26	C₂²	Dic₈₉₂	1	1	yes	characteristic
27	C₄	C₄⋊Dic₂₂₃	1	1	yes	characteristic
28	C₄	D₁₇₈₄	1	1	yes	characteristic
29	C₂	—	2	1	no	—
30	C₂	#20297238	1	1	yes	characteristic

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

N	H ≅ G/N	type
15. C₂₂₃	#368	semidirect

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