Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
372 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 372 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. #11728499 | C2 | semidirect |
| 5. C2×#89275 | C2 | semidirect |
| 6. C7×#1283 | C2 | semidirect |
| 7. #11725474 | C2 | semidirect |
| 68. #1283 | D7 | semidirect |
| 284. C7 | #8607 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11735964 | 2 |
| #11728509 | 2 |
| #11728499 | 2 |
| #11728179 | 2 |
| C2×#89275 | 2 |
| C7×#1283 | 2 |
| #11725474 | 2 |
| #8607 | 7 |