Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
254 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 254 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 |
|---|---|---|
| 13. #19151422 | C4 | semidirect |
| 116. C89 | #13117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022026 | 2 |
| #26021000 | 2 |
| #26018366 | 2 |
| #26018363 | 2 |
| #26018355 | 2 |
| #26018334 | 2 |
| C4×#108×C89 | 2 |
| #13117 | 89 |