Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
2502 conjugacy classes of subgroups; only the 371 normal subgroups are shown.
This group has 2502 conjugacy classes of subgroups — too many to draw. Only its 371 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. C2×#19151466 | C2 | semidirect |
| 3. #26018492 | C2 | semidirect |
| 4. C2×#383×C89 | C2 | semidirect |
| 8. C2×#15668009 | C4 | semidirect |
| 48. C42×C89 | C22⋊C4 | semidirect |
| 88. C2×#383 | D89 | semidirect |
| 90. C89 | #14661 | semidirect |
| 134. C42 | #13083551 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668009 | 2 |
| C2×#19151466 | 2 |
| #26018492 | 2 |
| C2×#383×C89 | 2 |
| #14661 | 89 |