Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
284 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 67 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. #11727049 | C2 | semidirect |
| 4. #11726798 | C2 | semidirect |
| 6. #11725370 | C2 | semidirect |
| 7. #11725311 | C2 | semidirect |
| 230. C7 | #12393 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11736864 | 2 |
| #11728606 | 2 |
| #11727049 | 2 |
| #11726798 | 2 |
| C7×D4⋊C16 | 2 |
| #11725370 | 2 |
| #11725311 | 2 |
| #12393 | 7 |