Subgroups — #16778217

Order 3328.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13129999	C₂	1	2	yes	maximal
2	D₁₃×C₆₄	C₂	1	1	yes	maximal, characteristic
3	#11718223	—	2	2	no	—
4	D₁₃×C₃₂	C₂²	1	1	yes	characteristic
5	C₁₃×C₆₄	C₄	1	1	yes	characteristic
6	#11718035	C₄	1	1	yes	characteristic
7	#88104	—	4	2	no	—
8	C₁₆×D₁₃	D₄	1	1	yes	characteristic
9	C₁₃×C₃₂	C₂×C₄	1	1	yes	characteristic
10	#88034	Q₈	1	1	yes	characteristic
11	#7547	—	13	1	no	maximal, Sylow
12	#6118	—	8	2	no	—
13	C₈×D₁₃	D₈	1	1	yes	characteristic
14	C₁₃×C₁₆	C₄⋊C₄	1	1	yes	characteristic
15	#6090	Q₁₆	1	1	yes	characteristic
16	C₂×C₆₄	—	13	1	no	—
17	#1425	—	13	2	no	—
18	C₄×D₁₃	D₁₆	1	1	yes	characteristic
19	#1057	—	16	2	no	—
20	C₈×C₁₃	#107	1	1	yes	characteristic
21	#1055	Q₃₂	1	1	yes	characteristic
22	C₂×C₃₂	—	13	1	no	—
23	#368	—	26	2	no	—
24	C₆₄	—	13	1	no	—
25	C₆₄	#261	1	1	yes	characteristic
26	C₂×D₁₃	Q₆₄	1	1	yes	characteristic
27	C₄×C₁₃	#366	1	1	yes	characteristic
28	Dic₁₃	D₃₂	1	1	yes	characteristic
29	C₂×C₁₆	—	13	1	no	—
30	#108	—	52	2	no	—
31	C₃₂	—	13	1	no	—
32	C₃₂	C₂×#261	1	1	yes	characteristic
33	C₂×C₁₃	#1423	1	1	yes	characteristic
34	D₁₃	—	2	1	no	—
35	M₁₆	—	104	2	no	—
36	C₂×C₈	—	13	1	no	—
37	C₁₆	—	13	1	no	—
38	C₁₆	C₄⋊#261	1	1	yes	characteristic
39	C₁₃	#7547	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₄	—	13	1	no	—
41	C₈	—	13	1	no	—
42	C₈	—	208	2	no	—
43	C₈	#88102	1	1	yes	characteristic
44	C₂²	—	13	1	no	—
45	C₄	—	13	1	no	—
46	C₄	#11718221	1	1	yes	characteristic
47	C₂	—	26	1	no	—
48	C₂	#13129997	1	1	yes	characteristic

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

N	H ≅ G/N	type
39. C₁₃	#7547	semidirect

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