Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
460 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 121 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. #11727794 | C2 | semidirect |
| 5. #11725503 | C2 | semidirect |
| 7. C2×#6511 | C4 | semidirect |
| 11. #90006 | C4 | semidirect |
| 16. #89696 | C4 | semidirect |
| 17. C2×C4×C7⋊C8 | C4 | semidirect |
| 20. #89343 | C4 | semidirect |
| 21. #89337 | C4 | semidirect |
| 282. C7 | #12633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11740720 | 2 |
| C7×#2126 | 2 |
| #11729574 | 2 |
| #11727794 | 2 |
| #11725503 | 2 |
| #12633 | 7 |