Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
314 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 2. #11727038 | C2 | semidirect |
| 3. #11726283 | C2 | semidirect |
| 4. C7×#1360 | C2 | semidirect |
| 5. #11725602 | C2 | semidirect |
| 6. #11725369 | C2 | semidirect |
| 7. #11725274 | C2 | semidirect |
| 68. #1360 | D7 | semidirect |
| 278. C7 | #11980 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11739254 | 2 |
| #11727038 | 2 |
| #11726283 | 2 |
| C7×#1360 | 2 |
| #11725602 | 2 |
| #11725369 | 2 |
| #11725274 | 2 |
| #11980 | 7 |