Finite Group DatabasebetaFinite Group DatabasebetaOrder 4704.
434 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 71 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. #72269288 | C2 | semidirect |
| 3. C7×#66728 | C2 | semidirect |
| 4. C7×#66627 | C2 | semidirect |
| 5. C2×C3×C4⋊(C7⋊D7) | C2 | semidirect |
| 10. C7×D84 | C22 | semidirect |
| 12. C7×Dic42 | C22 | semidirect |
| 15. C7×C3⋊(C7⋊C8) | C22 | semidirect |
| 16. C2×C4⋊(C7⋊D7) | D3 | semidirect |
| 39. #66728 | D7 | semidirect |
| 44. #66627 | D7 | semidirect |
| 70. D84 | C2×D7 | semidirect |
| 72. Dic42 | C2×D7 | semidirect |
| 83. C3⋊(C7⋊C8) | C2×D7 | semidirect |
| 85. C3×C72 | AGL(1,ℤ/8) | semidirect |
| 143. C72 | #932 | semidirect |
| 190. C3×C7 | #6471 | semidirect |
| 191. C3×C7 | #6512 | semidirect |
| 225. C7 | #10620860 | semidirect |
| 226. C7 | #10620874 | semidirect |
| 238. C3 | #13096291 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72269318 | 2 |
| #72269288 | 2 |
| C7×#66728 | 2 |
| C7×#66627 | 2 |
| C2×C3×C4⋊(C7⋊D7) | 2 |
| #13096291 | 3 |
| #10620874 | 7 |
| #10620860 | 7 |