Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
758 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 758 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 2. #26021943 | C2 | semidirect |
| 3. #26021907 | C2 | semidirect |
| 4. #26021893 | C2 | semidirect |
| 5. #26020804 | C2 | semidirect |
| 6. #26020779 | C2 | semidirect |
| 7. C89×#1891 | C2 | semidirect |
| 9. #19152337 | C4 | semidirect |
| 10. #19152332 | C4 | semidirect |
| 292. #1891 | D89 | semidirect |
| 293. C89 | #12758 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034527 | 2 |
| #26021943 | 2 |
| #26021907 | 2 |
| #26021893 | 2 |
| #26020804 | 2 |
| #26020779 | 2 |
| C89×#1891 | 2 |
| #12758 | 89 |