Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
316 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 316 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. #89349 | C2 | semidirect |
| 144. C7 | #1821 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊Dic7 | 2 |
| C7×#407 | 2 |
| #89979 | 2 |
| #89349 | 2 |
| #1821 | 7 |