Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
542 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 542 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. #26023137 | C2 | semidirect |
| 5. #26018159 | C2 | semidirect |
| 6. #26018138 | C2 | semidirect |
| 7. C89×#1826 | C2 | semidirect |
| 12. #19151641 | C4 | semidirect |
| 13. #19151602 | C4 | semidirect |
| 206. #1826 | D89 | semidirect |
| 210. C89 | #9367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030192 | 2 |
| #26023137 | 2 |
| #26021088 | 2 |
| #26018769 | 2 |
| #26018159 | 2 |
| #26018138 | 2 |
| C89×#1826 | 2 |
| #9367 | 89 |