Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
566 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 119 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. C22×Dic56 | C2 | semidirect |
| 4. C2×#89298 | C2 | semidirect |
| 5. #11725612 | C2 | semidirect |
| 103. C23×C7 | Q32 | semidirect |
| 215. C23 | Dic56 | semidirect |
| 240. C7 | #13306 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89888 | 2 |
| C22×Dic56 | 2 |
| C2×C7×C22⋊C16 | 2 |
| C2×#89298 | 2 |
| #11725612 | 2 |
| #13306 | 7 |