Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
600 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 4. #26020242 | C2 | semidirect |
| 5. #26020238 | C2 | semidirect |
| 6. #26018370 | C2 | semidirect |
| 7. C89×#1390 | C2 | semidirect |
| 10. C22×#13083551 | C4 | semidirect |
| 18. #19151471 | C4 | semidirect |
| 20. #19151453 | C4 | semidirect |
| 21. C22⋊C4×Dic89 | C4 | semidirect |
| 82. C23×D89 | C4⋊C4 | semidirect |
| 110. C22⋊Dic89 | C4⋊C4 | semidirect |
| 267. #1390 | D89 | semidirect |
| 268. C89 | #12795 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022915 | 2 |
| C2×#19151386 | 2 |
| C2×#19151384 | 2 |
| #26020242 | 2 |
| #26020238 | 2 |
| #26018370 | 2 |
| C89×#1390 | 2 |
| #12795 | 89 |