Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
670 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 670 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 |
|---|---|---|
| 1. C2×#89887 | C2 | semidirect |
| 2. C22×D112 | C2 | semidirect |
| 3. C2×C7×C22⋊C16 | C2 | semidirect |
| 4. C2×#89304 | C2 | semidirect |
| 5. #11725612 | C2 | semidirect |
| 38. C2×D56 | D4 | semidirect |
| 42. C2×C7×C16 | D4 | semidirect |
| 45. #6392 | D4 | semidirect |
| 50. C2×C22⋊C16 | D7 | semidirect |
| 105. C23×C7 | D16 | semidirect |
| 158. C2×C16 | C22⋊D7 | semidirect |
| 238. C23 | D112 | semidirect |
| 261. C7 | #13304 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89887 | 2 |
| C22×D112 | 2 |
| C2×C7×C22⋊C16 | 2 |
| C2×#89304 | 2 |
| #11725612 | 2 |
| #13304 | 7 |