Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
514 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 163 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. C2×C4×C7×C16 | C2 | semidirect |
| 3. C2×#89298 | C2 | semidirect |
| 5. #11727520 | C2 | semidirect |
| 16. #89468 | C4 | semidirect |
| 53. C2×C4×C16 | D7 | semidirect |
| 246. C7 | #13204 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89468 | 2 |
| C2×C4×C7×C16 | 2 |
| C2×#89298 | 2 |
| C2×#89304 | 2 |
| #11727520 | 2 |
| #13204 | 7 |