Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
438 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 438 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. #11727438 | C2 | semidirect |
| 3. #11726445 | C2 | semidirect |
| 5. C7×#1272 | C2 | semidirect |
| 6. #11725286 | C2 | semidirect |
| 66. #1272 | D7 | semidirect |
| 354. C7 | #7833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11734104 | 2 |
| #11727438 | 2 |
| #11726445 | 2 |
| #11726436 | 2 |
| C7×#1272 | 2 |
| #11725286 | 2 |
| #11725285 | 2 |
| #7833 | 7 |