Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
276 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 276 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 |
|---|---|---|
| 3. #11728437 | C2 | semidirect |
| 5. C7×#1382 | C2 | semidirect |
| 6. #11725613 | C2 | semidirect |
| 7. #11725531 | C2 | semidirect |
| 57. #1382 | D7 | semidirect |
| 242. C7 | #13499 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11729163 | 2 |
| #11728473 | 2 |
| #11728437 | 2 |
| #11728419 | 2 |
| C7×#1382 | 2 |
| #11725613 | 2 |
| #11725531 | 2 |
| #13499 | 7 |