Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
552 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 111 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. #26020279 | C2 | semidirect |
| 4. #26020030 | C2 | semidirect |
| 5. #26018824 | C2 | semidirect |
| 7. C89×#1996 | C2 | semidirect |
| 8. C22×#13083561 | C4 | semidirect |
| 16. C2×#15667943 | C4 | semidirect |
| 17. C2×#15667936 | C4 | semidirect |
| 18. C2×#15667932 | C4 | semidirect |
| 194. #10623494 | #99 | semidirect |
| 233. #1996 | D89 | semidirect |
| 239. C89 | #9786 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151829 | 2 |
| #26021088 | 2 |
| #26020279 | 2 |
| #26020030 | 2 |
| #26018824 | 2 |
| #26018819 | 2 |
| C89×#1996 | 2 |
| #9786 | 89 |