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. #26020340 | C2 | semidirect |
| 4. #26020330 | C2 | semidirect |
| 6. #26018128 | C2 | semidirect |
| 7. C89×#1305 | C2 | semidirect |
| 11. #19151929 | C4 | semidirect |
| 13. #19151912 | C4 | semidirect |
| 220. #1305 | 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 |
|---|---|
| #26030177 | 2 |
| #26029302 | 2 |
| #26020340 | 2 |
| #26020330 | 2 |
| #26018793 | 2 |
| #26018128 | 2 |
| C89×#1305 | 2 |
| #9521 | 89 |