Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
216 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 15. #89250 | C4 | semidirect |
| 16. #89249 | C4 | semidirect |
| 17. #89249 | C4 | semidirect |
| 18. C8×C7⋊C8 | C4 | semidirect |
| 187. C7 | #8803 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11727603 | 2 |
| C7×#1288 | 2 |
| #11725560 | 2 |
| #11725559 | 2 |
| #11725476 | 2 |
| #11725439 | 2 |
| #8803 | 7 |