Subgroups — #10597670

Order 624.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic
2	Dic₇₈	C₂	1	1	yes	maximal, characteristic
3	C₃⋊#1055	C₂	1	1	yes	maximal, characteristic
4	#6107	—	3	1	no	maximal, Hall
5	C₃×C₄×C₁₃	—	2	1	no	—
6	C₃×C₄×C₁₃	C₂²	1	1	yes	characteristic
7	Dic₃₉	—	2	1	no	—
8	Q₈×C₁₃	D₃	1	1	yes	characteristic
9	Dic₂₆	—	3	1	no	—
10	#1055	—	3	1	no	—
11	C₂×C₃×C₁₃	D₄	1	1	yes	characteristic
12	C₄×C₁₃	—	2	1	no	—
13	C₄×C₁₃	C₂×D₃	1	1	yes	characteristic
14	Dic₁₃	—	6	1	no	—
15	#216	—	13	1	no	maximal, Hall
16	C₃×C₁₃	Q₁₆	1	1	yes	characteristic, complemented, Hall
17	C₂×C₁₃	#67	1	1	yes	characteristic
18	C₃×Q₈	D₁₃	1	1	yes	characteristic
19	Dic₆	—	13	1	no	—
20	C₃⋊C₈	—	13	1	no	—
21	Q₁₆	—	39	1	no	Sylow
22	C₁₃	#216	1	1	yes	characteristic, complemented, Sylow
23	C₃×C₄	—	2	1	no	—
24	C₃×C₄	C₂×D₁₃	1	1	yes	characteristic
25	Dic₃	—	26	1	no	—
26	Q₈	—	39	1	no	—
27	Q₈	D₃₉	1	1	yes	characteristic
28	C₈	—	39	1	no	—
29	C₂×C₃	C₂²⋊D₁₃	1	1	yes	characteristic
30	C₄	—	2	1	no	—
31	C₄	—	78	1	no	—
32	C₄	C₂×D₃₉	1	1	yes	characteristic
33	C₃	#6107	1	1	yes	characteristic, complemented, Sylow
34	C₂	#64625	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.