Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
732 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 107 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. #26021232 | C2 | semidirect |
| 3. #26018972 | C2 | semidirect |
| 4. #26018889 | C2 | semidirect |
| 5. #26018761 | C2 | semidirect |
| 6. #26018760 | C2 | semidirect |
| 7. C89×#1557 | C2 | semidirect |
| 13. #19152253 | C4 | semidirect |
| 14. #19152252 | C4 | semidirect |
| 221. #1557 | D89 | semidirect |
| 225. C89 | #8494 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034650 | 2 |
| #26021232 | 2 |
| #26018972 | 2 |
| #26018889 | 2 |
| #26018761 | 2 |
| #26018760 | 2 |
| C89×#1557 | 2 |
| #8494 | 89 |