Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
420 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 420 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. #26020296 | C2 | semidirect |
| 4. #26018373 | C2 | semidirect |
| 5. C89×#1391 | C2 | semidirect |
| 6. C2×#15668020 | C4 | semidirect |
| 12. #19151621 | C4 | semidirect |
| 14. #19151564 | C4 | semidirect |
| 15. C2×#15667922 | C4 | semidirect |
| 150. #1391 | D89 | semidirect |
| 151. C89 | #12808 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028967 | 2 |
| #26021915 | 2 |
| #26020296 | 2 |
| #26018373 | 2 |
| C89×#1391 | 2 |
| #12808 | 89 |