Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
324 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 67 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. #11729170 | C2 | semidirect |
| 3. C2×#89244 | C2 | semidirect |
| 4. C7×C22⋊C32 | C2 | semidirect |
| 5. #11725402 | C2 | semidirect |
| 9. C2×Dic56 | C22 | semidirect |
| 13. C2×C7×C32 | C22 | semidirect |
| 14. #89299 | C22 | semidirect |
| 40. C22⋊C32 | D7 | semidirect |
| 70. C2×C32 | C2×D7 | semidirect |
| 112. C22×C7 | SD64 | semidirect |
| 168. C7 | #13664 | semidirect |
| 175. C22 | #89244 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D112 | 2 |
| #11729170 | 2 |
| C2×#89244 | 2 |
| C7×C22⋊C32 | 2 |
| #11725402 | 2 |
| #13664 | 7 |