Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
498 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 4. C7×#1286 | C2 | semidirect |
| 5. #11725552 | C2 | semidirect |
| 6. #11725521 | C2 | semidirect |
| 7. #11725437 | C2 | semidirect |
| 65. #1286 | D7 | semidirect |
| 310. C7 | #8765 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11731673 | 2 |
| #11728537 | 2 |
| #11728281 | 2 |
| C7×#1286 | 2 |
| #11725552 | 2 |
| #11725521 | 2 |
| #11725437 | 2 |
| #8765 | 7 |