Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
488 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 131 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. #11737060 | C2 | semidirect |
| 2. C4×C7×D16 | C2 | semidirect |
| 3. #11729224 | C2 | semidirect |
| 4. #11728642 | C2 | semidirect |
| 5. #11727080 | C2 | semidirect |
| 6. #11726955 | C2 | semidirect |
| 7. #11726953 | C2 | semidirect |
| 8. #11726809 | C2 | semidirect |
| 9. #11726799 | C2 | semidirect |
| 72. C4×D16 | D7 | semidirect |
| 256. C7 | #33922 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11737060 | 2 |
| C4×C7×D16 | 2 |
| #11729224 | 2 |
| #11728642 | 2 |
| #11727080 | 2 |
| #11726955 | 2 |
| #11726953 | 2 |
| #11726809 | 2 |
| #11726799 | 2 |
| #33922 | 7 |