Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
140 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 51 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 |
|---|---|---|
| 125. C7 | #1704 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #89623 | 2 |
| #89622 | 2 |
| #89453 | 2 |
| #89451 | 2 |
| C7×#334 | 2 |
| #89281 | 2 |
| #89276 | 2 |
| #1704 | 7 |