Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
830 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 830 conjugacy classes of subgroups — too many to draw. Only its 111 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. C2×#89511 | C2 | semidirect |
| 5. #11727178 | C2 | semidirect |
| 6. C2×#89247 | C2 | semidirect |
| 7. #11725480 | C2 | semidirect |
| 452. C7 | #9965 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11740124 | 2 |
| C2×#89812 | 2 |
| C2×#89511 | 2 |
| C2×C7×#327 | 2 |
| #11727178 | 2 |
| C2×#89247 | 2 |
| #11725480 | 2 |
| #9965 | 7 |