Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
576 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 576 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 |
|---|---|---|
| 2. #26023362 | C2 | semidirect |
| 3. #26018875 | C2 | semidirect |
| 4. #26018761 | C2 | semidirect |
| 5. #26018759 | C2 | semidirect |
| 6. #26018146 | C2 | semidirect |
| 7. C89×#1300 | C2 | semidirect |
| 12. #19151992 | C4 | semidirect |
| 13. #19151987 | C4 | semidirect |
| 43. #15668012 | C2×C4 | semidirect |
| 44. #15668009 | C2×C4 | semidirect |
| 76. #97×C89 | C2×C4 | semidirect |
| 233. #1300 | D89 | semidirect |
| 234. C89 | #9441 | semidirect |
| 298. #97 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030718 | 2 |
| #26023362 | 2 |
| #26018875 | 2 |
| #26018761 | 2 |
| #26018759 | 2 |
| #26018146 | 2 |
| C89×#1300 | 2 |
| #9441 | 89 |