Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
306 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 93 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. #26021856 | C2 | semidirect |
| 5. #26021033 | C2 | semidirect |
| 6. #26018357 | C2 | semidirect |
| 7. C89×#1389 | C2 | semidirect |
| 15. #19151413 | C4 | semidirect |
| 16. #19151410 | C4 | semidirect |
| 145. #1389 | D89 | semidirect |
| 147. C89 | #13156 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021999 | 2 |
| C2×#19151409 | 2 |
| #26021856 | 2 |
| #26021148 | 2 |
| #26021033 | 2 |
| #26018357 | 2 |
| C89×#1389 | 2 |
| #13156 | 89 |