Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
492 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 492 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. #26021196 | C2 | semidirect |
| 5. #26018802 | C2 | semidirect |
| 6. #26018107 | C2 | semidirect |
| 7. C89×#1288 | C2 | semidirect |
| 10. #19151992 | C4 | semidirect |
| 11. #19151958 | C4 | semidirect |
| 36. #15668012 | C2×C4 | semidirect |
| 37. #15668012 | C2×C4 | semidirect |
| 71. #97×C89 | C2×C4 | semidirect |
| 210. #1288 | D89 | semidirect |
| 212. C89 | #9379 | semidirect |
| 273. #97 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031257 | 2 |
| #26023062 | 2 |
| #26021196 | 2 |
| #26018849 | 2 |
| #26018802 | 2 |
| #26018107 | 2 |
| C89×#1288 | 2 |
| #9379 | 89 |