Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
908 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 908 conjugacy classes of subgroups — too many to draw. Only its 147 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 |
|---|---|---|
| 4. #11727279 | C2 | semidirect |
| 5. #11725430 | C2 | semidirect |
| 18. #89719 | C4 | semidirect |
| 31. C22×Dic14 | C2×C4 | semidirect |
| 49. C7⋊#95 | C2×C4 | semidirect |
| 140. C23×C7 | #103 | semidirect |
| 318. C23 | #6384 | semidirect |
| 354. C7 | #9013 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2315 | 2 |
| C2×#89719 | 2 |
| C2×#89320 | 2 |
| #11727279 | 2 |
| #11725430 | 2 |
| #9013 | 7 |