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. #26021233 | C2 | semidirect |
| 5. #26018724 | C2 | semidirect |
| 6. #26018142 | C2 | semidirect |
| 7. C89×#1300 | C2 | semidirect |
| 10. #19152007 | C4 | semidirect |
| 11. #19151992 | C4 | semidirect |
| 12. #19151967 | C4 | semidirect |
| 13. #19151958 | C4 | semidirect |
| 204. #1300 | D89 | semidirect |
| 206. C89 | #8998 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030858 | 2 |
| #26029424 | 2 |
| #26021233 | 2 |
| #26018736 | 2 |
| #26018724 | 2 |
| #26018142 | 2 |
| C89×#1300 | 2 |
| #8998 | 89 |