Finite Group DatabasebetaFinite Group DatabasebetaOrder 4704.
434 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 60 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×#66632 | C2 | semidirect |
| 2. #72269313 | C2 | semidirect |
| 3. #72269294 | C2 | semidirect |
| 4. C3×C7×#1142 | C2 | semidirect |
| 5. #72254247 | C2 | semidirect |
| 6. #72254206 | C2 | semidirect |
| 7. D4×C3⋊(C7⋊D7) | C2 | semidirect |
| 14. C7×D84 | C22 | semidirect |
| 15. C3×C7×Dic14 | C22 | semidirect |
| 18. C7×C3⋊(C7⋊C8) | C22 | semidirect |
| 19. C3×C7×C7⋊C8 | C22 | semidirect |
| 22. C7×#1142 | D3 | semidirect |
| 43. C7×Dic14 | C2×D3 | semidirect |
| 47. C7×C7⋊C8 | C2×D3 | semidirect |
| 55. #66632 | D7 | semidirect |
| 59. C3×#1142 | D7 | semidirect |
| 92. D84 | C2×D7 | semidirect |
| 98. C3×Dic14 | C2×D7 | semidirect |
| 102. C3⋊(C7⋊C8) | C2×D7 | semidirect |
| 103. C3×C7⋊C8 | C2×D7 | semidirect |
| 105. C3×C72 | AGL(1,ℤ/8) | semidirect |
| 114. #1142 | D21 | semidirect |
| 171. Dic14 | C2×D21 | semidirect |
| 175. C7⋊C8 | C2×D21 | semidirect |
| 176. C72 | #914 | semidirect |
| 233. C3×C7 | #6474 | semidirect |
| 234. C3×C7 | #6477 | semidirect |
| 276. C7 | #10621062 | semidirect |
| 277. C7 | #10621397 | semidirect |
| 291. C3 | #13096375 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#66632 | 2 |
| #72269313 | 2 |
| #72269294 | 2 |
| C3×C7×#1142 | 2 |
| #72254247 | 2 |
| #72254206 | 2 |
| D4×C3⋊(C7⋊D7) | 2 |
| #13096375 | 3 |
| #10621397 | 7 |
| #10621062 | 7 |