Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
284 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 4. C2×#89284 | C2 | semidirect |
| 5. #11725538 | C2 | semidirect |
| 6. #11725534 | C2 | semidirect |
| 7. #11725529 | C2 | semidirect |
| 253. C7 | #13495 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#1816 | 2 |
| #11729770 | 2 |
| #11729758 | 2 |
| C2×#89284 | 2 |
| #11725538 | 2 |
| #11725534 | 2 |
| #11725529 | 2 |
| #13495 | 7 |