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×C7×D16 | C2 | semidirect |
| 2. C2×#89929 | C2 | semidirect |
| 3. C2×#89357 | C2 | semidirect |
| 4. C2×(C2×D7)⋊C16 | C2 | semidirect |
| 5. #11725612 | C2 | semidirect |
| 28. C2×C7×D8 | D4 | semidirect |
| 41. C2×C7×C16 | D4 | semidirect |
| 44. #6392 | D4 | semidirect |
| 47. C22×D16 | D7 | semidirect |
| 113. C22×D7 | D16 | semidirect |
| 143. C2×D8 | C22⋊D7 | semidirect |
| 158. C2×C16 | C22⋊D7 | 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×C7×D16 | 2 |
| C2×#89929 | 2 |
| C2×#89357 | 2 |
| C2×(C2×D7)⋊C16 | 2 |
| #11725612 | 2 |
| #13304 | 7 |