Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
602 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 602 conjugacy classes of subgroups — too many to draw. Only its 155 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. C4×C7×C4⋊C8 | C2 | semidirect |
| 3. C2×#89276 | C2 | semidirect |
| 5. #11727146 | C2 | semidirect |
| 48. C4×C4⋊C8 | D7 | semidirect |
| 246. C7 | #9699 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11730758 | 2 |
| C4×C7×C4⋊C8 | 2 |
| C2×#89276 | 2 |
| C2×#89280 | 2 |
| #11727146 | 2 |
| #9699 | 7 |