Subgroups — C₇×#1840 #11730309

Order 896.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#376	C₂	1	1	yes	maximal, characteristic
2	C₇×#336	C₂	1	6	yes	maximal
3	C₂²×C₇×C₈	C₂²	1	4	yes	—
4	C₂×C₄²×C₇	C₂²	1	3	yes	—
5	C₇×#95	C₄	1	4	yes	—
6	#1840	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₂²×C₄×C₇	C₂×C₄	1	6	yes	—
8	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
9	C₂×C₇×C₈	—	2	12	no	—
10	C₄²×C₇	—	2	6	no	—
11	#376	C₂×C₇	1	1	yes	characteristic
12	#336	C₂×C₇	1	6	yes	—
13	C₂³×C₇	C₂²×C₄	1	1	yes	characteristic
14	C₂×C₄×C₇	—	2	6	no	—
15	C₂×C₄×C₇	—	2	12	no	—
16	C₂×C₄×C₇	#41	1	6	yes	—
17	C₇×C₈	—	4	4	no	—
18	C₂²×C₈	C₂²×C₇	1	4	yes	—
19	C₂×C₄²	C₂²×C₇	1	3	yes	—
20	#95	C₄×C₇	1	4	yes	—
21	C₂²×C₇	#117	1	3	yes	—
22	C₂²×C₇	#131	1	4	yes	—
23	C₄×C₇	—	4	6	no	—
24	C₄×C₇	#126	1	4	yes	—
25	C₂²×C₄	C₂×C₄×C₇	1	6	yes	—
26	C₂²×C₄	C₂³×C₇	1	1	yes	characteristic
27	C₂×C₈	—	2	12	no	—
28	C₄²	—	2	6	no	—
29	C₂×C₇	#383	1	1	yes	characteristic
30	C₂×C₇	#433	1	6	yes	—
31	C₂³	C₂²×C₄×C₇	1	1	yes	characteristic
32	C₂×C₄	—	2	6	no	—
33	C₂×C₄	—	2	12	no	—
34	C₂×C₄	C₇×#41	1	6	yes	—
35	C₈	—	4	4	no	—
36	C₇	#1840	1	1	yes	characteristic, direct product factor, Sylow
37	C₂²	C₇×#117	1	3	yes	—
38	C₂²	C₇×#131	1	4	yes	—
39	C₄	—	4	6	no	—
40	C₄	C₇×#126	1	4	yes	—
41	C₂	C₇×#383	1	1	yes	characteristic
42	C₂	C₇×#433	1	6	yes	—

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

N	H ≅ G/N	type
6. #1840	C₇	direct (N × H)
36. C₇	#1840	direct (N × H)

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