Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
626 conjugacy classes of subgroups; only the 201 normal subgroups are shown.
This group has 626 conjugacy classes of subgroups — too many to draw. Only its 201 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. #26020967 | C2 | semidirect |
| 4. #26020806 | C2 | semidirect |
| 6. #26020397 | C2 | semidirect |
| 7. C89×#1843 | C2 | semidirect |
| 121. #1843 | D89 | semidirect |
| 123. C89 | #23381 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023550 | 2 |
| #26020967 | 2 |
| #26020857 | 2 |
| #26020806 | 2 |
| #26020433 | 2 |
| #26020397 | 2 |
| C89×#1843 | 2 |
| #23381 | 89 |