Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
474 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 10. #19151890 | C4 | semidirect |
| 11. #19151805 | C4 | semidirect |
| 94. C4×Dic89 | Q16 | semidirect |
| 186. C89 | #9236 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030287 | 2 |
| #26022726 | 2 |
| #26021230 | 2 |
| #26018682 | 2 |
| #26018155 | 2 |
| #26018084 | 2 |
| C89×#1503 | 2 |
| #9236 | 89 |