Subgroups — #4449

Order 192.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₂₄	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄₈	C₂	1	1	yes	maximal, characteristic
3	C₃×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	SD₆₄	—	3	1	no	maximal, Sylow
5	Dic₁₂	—	2	1	no	—
6	D₂₄	—	2	1	no	—
7	C₃×C₁₆	C₂²	1	1	yes	characteristic
8	Q₃₂	—	3	1	no	—
9	D₁₆	—	3	1	no	—
10	C₃₂	D₃	1	1	yes	characteristic, complemented
11	D₁₂	—	4	1	no	—
12	Dic₆	—	4	1	no	—
13	C₃×C₈	D₄	1	1	yes	characteristic
14	Q₁₆	—	6	1	no	—
15	D₈	—	6	1	no	—
16	C₁₆	C₂×D₃	1	1	yes	characteristic
17	C₂×D₃	—	8	1	no	—
18	C₃×C₄	D₈	1	1	yes	characteristic
19	Dic₃	—	8	1	no	—
20	Q₈	—	12	1	no	—
21	D₄	—	12	1	no	—
22	C₈	D₁₂	1	1	yes	characteristic
23	C₂×C₃	D₁₆	1	1	yes	characteristic
24	D₃	—	16	1	no	—
25	C₂²	—	24	1	no	—
26	C₄	—	24	1	no	—
27	C₄	D₂₄	1	1	yes	characteristic
28	C₃	SD₆₄	1	1	yes	characteristic, complemented, Sylow
29	C₂	—	48	1	no	—
30	C₂	D₄₈	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.