Finite Group DatabasebetaFinite Group DatabasebetaOrder 4704.
434 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 59 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. #72269318 | C2 | semidirect |
| 2. C7×#66632 | C2 | semidirect |
| 3. #72269288 | C2 | semidirect |
| 4. C7×#66633 | C2 | semidirect |
| 5. #72254252 | C2 | semidirect |
| 6. #72254211 | C2 | semidirect |
| 7. C3×D4×C7⋊D7 | C2 | semidirect |
| 11. C7×D84 | C22 | semidirect |
| 12. C7×Dic42 | C22 | semidirect |
| 18. C7×C3⋊(C7⋊C8) | C22 | semidirect |
| 19. C7×C3⋊(C7⋊C8) | C22 | semidirect |
| 20. D4×C7⋊D7 | D3 | semidirect |
| 53. #66633 | D7 | semidirect |
| 54. #66632 | D7 | semidirect |
| 84. D84 | C2×D7 | semidirect |
| 85. Dic42 | C2×D7 | semidirect |
| 101. C3⋊(C7⋊C8) | C2×D7 | semidirect |
| 102. C3⋊(C7⋊C8) | C2×D7 | semidirect |
| 105. C3×C72 | AGL(1,ℤ/8) | semidirect |
| 176. C72 | #932 | semidirect |
| 233. C3×C7 | #6474 | semidirect |
| 234. C3×C7 | #6477 | semidirect |
| 276. C7 | #10621051 | semidirect |
| 277. C7 | #10621053 | semidirect |
| 291. C3 | #13096375 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72269318 | 2 |
| C7×#66632 | 2 |
| #72269288 | 2 |
| C7×#66633 | 2 |
| #72254252 | 2 |
| #72254211 | 2 |
| C3×D4×C7⋊D7 | 2 |
| #13096375 | 3 |
| #10621053 | 7 |
| #10621051 | 7 |