Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
478 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 9. #19151928 | C4 | semidirect |
| 12. #19151754 | C4 | semidirect |
| 217. C89 | #9342 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031073 | 2 |
| #26023415 | 2 |
| #26018785 | 2 |
| #26018771 | 2 |
| #26018158 | 2 |
| #26018105 | 2 |
| C89×#1996 | 2 |
| #9342 | 89 |