Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
670 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 670 conjugacy classes of subgroups — too many to draw. Only its 117 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. C22×D112 | C2 | semidirect |
| 2. C2×#89655 | C2 | semidirect |
| 3. C2×(C2×D7)⋊C16 | C2 | semidirect |
| 4. C2×#89286 | C2 | semidirect |
| 5. C7×#1380 | C2 | semidirect |
| 32. C2×D56 | D4 | semidirect |
| 40. C2×C7×C16 | D4 | semidirect |
| 42. C7×#107 | D4 | semidirect |
| 51. #1380 | D7 | semidirect |
| 113. C22×D7 | D16 | semidirect |
| 158. C2×C16 | D28 | semidirect |
| 160. #107 | D28 | semidirect |
| 261. C7 | #13304 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D112 | 2 |
| C2×#89655 | 2 |
| C2×(C2×D7)⋊C16 | 2 |
| C2×#89286 | 2 |
| C7×#1380 | 2 |
| #13304 | 7 |