Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
558 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 119 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 |
|---|---|---|
| 3. #26018648 | C2 | semidirect |
| 4. #26018084 | C2 | semidirect |
| 55. C2×Dic178 | M16 | semidirect |
| 72. C4×Dic89 | M16 | semidirect |
| 158. C89 | #8961 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029293 | 2 |
| C4×#15667999 | 2 |
| #26018648 | 2 |
| #26018084 | 2 |
| C89×#1460 | 2 |
| #8961 | 89 |