Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
414 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 414 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 |
|---|---|---|
| 3. #26018816 | C2 | semidirect |
| 5. #26018150 | C2 | semidirect |
| 6. #26018134 | C2 | semidirect |
| 7. C89×#1531 | C2 | semidirect |
| 9. #19152004 | C4 | semidirect |
| 10. #19151990 | C4 | semidirect |
| 11. #19151966 | C4 | semidirect |
| 12. #19151960 | C4 | semidirect |
| 201. #1531 | D89 | semidirect |
| 206. C89 | #9431 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030955 | 2 |
| #26029246 | 2 |
| #26018816 | 2 |
| #26018791 | 2 |
| #26018150 | 2 |
| #26018134 | 2 |
| C89×#1531 | 2 |
| #9431 | 89 |