Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
156 conjugacy classes of subgroups; only the 25 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 25 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 |
|---|---|---|
| 7. #89452 | C4 | semidirect |
| 10. #89250 | C4 | semidirect |
| 114. C7 | #7533 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11729031 | 2 |
| C7×#1408 | 2 |
| #11725598 | 2 |
| #7533 | 7 |