Finite Group DatabasebetaFinite Group DatabasebetaOrder 4704.
434 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C7×#66562 | C2 | semidirect |
| 2. C7×#66567 | C2 | semidirect |
| 3. C7×#66728 | C2 | semidirect |
| 4. C3×C7×#1136 | C2 | semidirect |
| 5. C2×C72×D12 | C2 | semidirect |
| 10. C7×D84 | C22 | semidirect |
| 12. C7×Dic42 | C22 | semidirect |
| 15. C3×C7×C7⋊C8 | C22 | semidirect |
| 20. C7×#1136 | D3 | semidirect |
| 22. #10620866 | C7 | direct (N × H) |
| 38. C7×C7⋊C8 | C2×D3 | semidirect |
| 39. #66728 | C2×C7 | semidirect |
| 42. C2×C7×D12 | D7 | semidirect |
| 43. C2×C7×D12 | C2×C7 | semidirect |
| 47. C3×#1136 | C2×C7 | semidirect |
| 48. #66567 | C2×C7 | semidirect |
| 49. #66562 | C2×C7 | semidirect |
| 70. D84 | C22×C7 | semidirect |
| 72. Dic42 | C22×C7 | semidirect |
| 84. C3×C7⋊C8 | C22×C7 | semidirect |
| 85. C3×C72 | AGL(1,ℤ/8) | semidirect |
| 96. #1136 | D3×C7 | semidirect |
| 142. C7⋊C8 | C2×D3×C7 | semidirect |
| 143. C72 | #908 | semidirect |
| 145. C2×D12 | C7×D7 | semidirect |
| 190. C3×C7 | #6495 | semidirect |
| 191. C3×C7 | C7×AGL(1,ℤ/8) | semidirect |
| 225. C7 | #10620866 | direct (N × H) |
| 226. C7 | C7×#908 | semidirect |
| 238. C3 | C7×#6495 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#66562 | 2 |
| C7×#66567 | 2 |
| C7×#66728 | 2 |
| C3×C7×#1136 | 2 |
| C2×C72×D12 | 2 |
| C7×#6495 | 3 |
| C7×#908 | 7 |
| #10620866 | 7 |