Subgroups — #4522

Order 192.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×Q₃₂	C₂	1	1	yes	maximal, characteristic
2	Dic₂₄	C₂	1	1	yes	maximal, characteristic
3	C₃⋊C₃₂	C₂	1	1	yes	maximal, characteristic
4	Q₆₄	—	3	1	no	maximal, Sylow
5	C₃×Q₁₆	—	2	1	no	—
6	Dic₁₂	—	2	1	no	—
7	C₃×C₁₆	C₂²	1	1	yes	characteristic
8	Q₃₂	—	3	1	no	—
9	Q₃₂	D₃	1	1	yes	characteristic
10	C₃₂	—	3	1	no	—
11	C₃×Q₈	—	4	1	no	—
12	Dic₆	—	4	1	no	—
13	C₃×C₈	D₄	1	1	yes	characteristic
14	Q₁₆	—	2	1	no	—
15	Q₁₆	—	6	1	no	—
16	C₁₆	C₂×D₃	1	1	yes	characteristic
17	C₃×C₄	—	8	1	no	—
18	C₃×C₄	D₈	1	1	yes	characteristic
19	Dic₃	—	8	1	no	—
20	Q₈	—	4	1	no	—
21	Q₈	—	12	1	no	—
22	C₈	#67	1	1	yes	characteristic
23	C₂×C₃	D₁₆	1	1	yes	characteristic
24	C₄	—	8	1	no	—
25	C₄	—	24	1	no	—
26	C₄	#213	1	1	yes	characteristic
27	C₃	Q₆₄	1	1	yes	characteristic, complemented, Sylow
28	C₂	#826	1	1	yes	characteristic

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

N	H ≅ G/N	type
27. C₃	Q₆₄	semidirect

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