Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
252 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 18. #6453 | C4 | semidirect |
| 172. C7 | #1991 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6453 | 2 |
| C2×C8×Dic7 | 2 |
| #89749 | 2 |
| C7×#340 | 2 |
| #89346 | 2 |
| #89324 | 2 |
| #1991 | 7 |