Subgroups — #13092255

Order 1472.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×D₁₆	C₂	1	1	yes	maximal, characteristic
2	Dic₁₈₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃⋊C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	D₈×C₂₃	—	2	1	no	—
5	Dic₉₂	—	2	1	no	—
6	C₁₆×C₂₃	C₂²	1	1	yes	characteristic
7	D₄×C₂₃	—	4	1	no	—
8	Dic₄₆	—	4	1	no	—
9	C₈×C₂₃	D₄	1	1	yes	characteristic
10	C₂²×C₂₃	—	8	1	no	—
11	C₄×C₂₃	D₈	1	1	yes	characteristic
12	Dic₂₃	—	8	1	no	—
13	SD₆₄	—	23	1	no	maximal, Sylow
14	C₂×C₂₃	—	16	1	no	—
15	C₂×C₂₃	D₁₆	1	1	yes	characteristic
16	Q₃₂	—	23	1	no	—
17	D₁₆	D₂₃	1	1	yes	characteristic
18	C₃₂	—	23	1	no	—
19	C₂₃	SD₆₄	1	1	yes	characteristic, complemented, Sylow
20	Q₁₆	—	46	1	no	—
21	D₈	—	2	1	no	—
22	C₁₆	C₂×D₂₃	1	1	yes	characteristic
23	Q₈	—	92	1	no	—
24	D₄	—	4	1	no	—
25	C₈	C₂²⋊D₂₃	1	1	yes	characteristic
26	C₂²	—	8	1	no	—
27	C₄	—	184	1	no	—
28	C₄	#67272	1	1	yes	characteristic
29	C₂	—	16	1	no	—
30	C₂	#10625008	1	1	yes	characteristic

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

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