Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
234 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 12. #19151374 | C4 | semidirect |
| 13. C4×#13083549 | C4 | semidirect |
| 113. C89 | #12893 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021849 | 2 |
| #26020376 | 2 |
| #26018355 | 2 |
| #26018353 | 2 |
| #26018349 | 2 |
| #26018347 | 2 |
| C89×#1833 | 2 |
| #12893 | 89 |