Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
472 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 472 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. #26020332 | C2 | semidirect |
| 5. #26018158 | C2 | semidirect |
| 6. #26018129 | C2 | semidirect |
| 7. C89×#1824 | C2 | semidirect |
| 10. #19151928 | C4 | semidirect |
| 12. #19151911 | C4 | semidirect |
| 217. #1824 | D89 | semidirect |
| 222. C89 | #9521 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030175 | 2 |
| #26029297 | 2 |
| #26020332 | 2 |
| #26018793 | 2 |
| #26018158 | 2 |
| #26018129 | 2 |
| C89×#1824 | 2 |
| #9521 | 89 |