Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
500 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 83 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. C7×#1459 | C2 | semidirect |
| 3. C4×#6408 | C2 | semidirect |
| 4. #11725255 | C2 | semidirect |
| 5. #11725254 | C2 | semidirect |
| 7. C2×#6438 | C4 | semidirect |
| 15. #89732 | C4 | semidirect |
| 17. #89719 | C4 | semidirect |
| 19. #89709 | C4 | semidirect |
| 60. #1459 | D7 | semidirect |
| 354. C7 | #11730 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11739866 | 2 |
| C7×#1459 | 2 |
| C4×#6408 | 2 |
| #11725255 | 2 |
| #11725254 | 2 |
| #11730 | 7 |