Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
418 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 418 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. #26021204 | C2 | semidirect |
| 4. #26018977 | C2 | semidirect |
| 6. #26018121 | C2 | semidirect |
| 7. C89×#1285 | C2 | semidirect |
| 10. #19152007 | C4 | semidirect |
| 11. #19151958 | C4 | semidirect |
| 195. #1285 | D89 | semidirect |
| 196. C89 | #9375 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031475 | 2 |
| #26029393 | 2 |
| #26021204 | 2 |
| #26018977 | 2 |
| #26018775 | 2 |
| #26018121 | 2 |
| C89×#1285 | 2 |
| #9375 | 89 |