Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
422 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 109 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. #89864 | C4 | semidirect |
| 17. #89853 | C4 | semidirect |
| 87. C2×C7×C8 | Q16 | semidirect |
| 235. C2×C8 | #1144 | semidirect |
| 288. C7 | #9290 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11740667 | 2 |
| #11735925 | 2 |
| C7×#1993 | 2 |
| #11729529 | 2 |
| #11727300 | 2 |
| #11725466 | 2 |
| #11725437 | 2 |
| #9290 | 7 |