Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
486 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 2. #26020039 | C2 | semidirect |
| 3. #26018571 | C2 | semidirect |
| 4. #26018276 | C2 | semidirect |
| 5. #26018250 | C2 | semidirect |
| 6. #26018248 | C2 | semidirect |
| 7. C89×#1352 | C2 | semidirect |
| 8. C2×#15667987 | C4 | semidirect |
| 12. #19151536 | C4 | semidirect |
| 13. #19151516 | C4 | semidirect |
| 19. #19151460 | C4 | semidirect |
| 223. #1352 | D89 | semidirect |
| 226. C89 | #11729 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26026142 | 2 |
| #26020039 | 2 |
| #26018571 | 2 |
| #26018276 | 2 |
| #26018250 | 2 |
| #26018248 | 2 |
| C89×#1352 | 2 |
| #11729 | 89 |