Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
682 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 682 conjugacy classes of subgroups — too many to draw. Only its 187 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×Dic56 | C2 | semidirect |
| 4. C2×C7×#367 | C2 | semidirect |
| 5. C2×#89287 | C2 | semidirect |
| 6. #11727103 | C2 | direct (N × H) |
| 15. C2×Dic56 | C22 | semidirect |
| 20. C7×#367 | C22 | semidirect |
| 21. #89287 | C22 | semidirect |
| 53. C2×#367 | D7 | semidirect |
| 99. #367 | C2×D7 | semidirect |
| 194. C2×C7 | #2219 | semidirect |
| 222. C7 | C2×#2219 | semidirect |
| 236. C2 | #11727103 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic56 | 2 |
| C22×#6372 | 2 |
| C2×#89659 | 2 |
| C2×C7×#367 | 2 |
| C2×#89287 | 2 |
| #11727103 | 2 |
| C2×#2219 | 7 |