Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
630 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 630 conjugacy classes of subgroups — too many to draw. Only its 147 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 |
|---|---|---|
| 8. #19151504 | C4 | semidirect |
| 9. #19151496 | C4 | semidirect |
| 172. C89 | #9152 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028591 | 2 |
| #26020320 | 2 |
| C2×#19151334 | 2 |
| #26018131 | 2 |
| C2×#382×C89 | 2 |
| #9152 | 89 |