Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
466 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 105 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. C2×#89489 | C2 | semidirect |
| 3. C7×#1975 | C2 | semidirect |
| 4. #11729834 | C2 | semidirect |
| 5. #11728441 | C2 | semidirect |
| 6. #11725540 | C2 | semidirect |
| 7. #11725470 | C2 | semidirect |
| 18. #89951 | C4 | semidirect |
| 19. #89919 | C4 | semidirect |
| 78. #1975 | D7 | semidirect |
| 341. C7 | #13024 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11741339 | 2 |
| C2×#89489 | 2 |
| C7×#1975 | 2 |
| #11729834 | 2 |
| #11728441 | 2 |
| #11725540 | 2 |
| #11725470 | 2 |
| #13024 | 7 |