Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
326 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 326 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 |
|---|---|---|
| 4. #11725353 | C2 | semidirect |
| 6. #90161 | C4 | semidirect |
| 13. #89828 | C4 | semidirect |
| 15. C2×C4×C7⋊C8 | C4 | semidirect |
| 243. C7 | #13602 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11740726 | 2 |
| C7×#2132 | 2 |
| #11729573 | 2 |
| #11725353 | 2 |
| #13602 | 7 |