Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
252 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 93 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. #89897 | C2 | semidirect |
| 5. #89353 | C2 | semidirect |
| 117. C7 | #1858 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #90510 | 2 |
| C7×#413 | 2 |
| #90006 | 2 |
| #89897 | 2 |
| #89353 | 2 |
| #1858 | 7 |