Subgroups — #4513

Order 192.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×M₃₂	C₂	1	1	yes	maximal, characteristic
2	#819	C₂	1	1	yes	maximal, characteristic
3	#817	C₂	1	1	yes	maximal, characteristic
4	#365	—	3	1	no	maximal, Sylow
5	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
6	C₄⋊Dic₃	—	2	1	no	—
7	#208	—	2	1	no	—
8	C₃×C₁₆	C₄	1	2	yes	complemented
9	M₃₂	D₃	1	1	yes	characteristic
10	#108	—	3	1	no	—
11	#106	—	3	1	no	—
12	C₂×C₃×C₄	D₄	1	1	yes	characteristic
13	C₂×Dic₃	—	4	1	no	—
14	C₃×C₈	C₂×C₄	1	1	yes	characteristic
15	C₃×C₈	Q₈	1	1	yes	characteristic
16	C₃⋊C₈	—	4	1	no	—
17	M₁₆	—	6	1	no	—
18	C₂×C₈	C₂×D₃	1	1	yes	characteristic
19	C₄⋊C₄	—	6	1	no	—
20	C₁₆	Dic₃	1	2	yes	complemented
21	C₂²×C₃	SD₁₆	1	1	yes	characteristic
22	C₃×C₄	C₄⋊C₄	1	1	yes	characteristic
23	C₃×C₄	SD₁₆	1	1	yes	characteristic
24	Dic₃	—	8	1	no	—
25	C₂×C₄	—	12	1	no	—
26	C₂×C₄	D₁₂	1	1	yes	characteristic
27	C₈	—	12	1	no	—
28	C₈	Dic₆	1	1	yes	characteristic
29	C₈	C₂×Dic₃	1	1	yes	characteristic
30	C₂×C₃	—	2	1	no	—
31	C₂×C₃	#106	1	1	yes	characteristic
32	C₂²	#204	1	1	yes	characteristic
33	C₄	—	24	1	no	—
34	C₄	#204	1	1	yes	characteristic
35	C₄	C₄⋊Dic₃	1	1	yes	characteristic
36	C₃	#365	1	1	yes	characteristic, complemented, Sylow
37	C₂	—	2	1	no	—
38	C₂	#817	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.