Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
184 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 145. C7 | #2082 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6398 | 2 |
| #89897 | 2 |
| #89892 | 2 |
| #89776 | 2 |
| C7×#344 | 2 |
| #89351 | 2 |
| #89326 | 2 |
| #2082 | 7 |