Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
530 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 99 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. #26021170 | C2 | semidirect |
| 3. #26018850 | C2 | semidirect |
| 4. #26018798 | C2 | semidirect |
| 5. #26018116 | C2 | semidirect |
| 6. #26018108 | C2 | semidirect |
| 7. C89×#2337 | C2 | semidirect |
| 9. #19151988 | C4 | semidirect |
| 10. #19151957 | C4 | semidirect |
| 35. #15668012 | C2×C4 | semidirect |
| 36. #15668009 | C2×C4 | semidirect |
| 52. #15667923 | C2×C4 | semidirect |
| 223. #2337 | D89 | semidirect |
| 229. C89 | #9381 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031239 | 2 |
| #26021170 | 2 |
| #26018850 | 2 |
| #26018798 | 2 |
| #26018116 | 2 |
| #26018108 | 2 |
| C89×#2337 | 2 |
| #9381 | 89 |