Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
706 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 706 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 1. #26029293 | C2 | semidirect |
| 2. #26020244 | C2 | semidirect |
| 3. #26018920 | C2 | semidirect |
| 4. #26018155 | C2 | semidirect |
| 24. C4⋊#10623494 | D4 | semidirect |
| 158. C89 | #9405 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029293 | 2 |
| #26020244 | 2 |
| #26018920 | 2 |
| #26018155 | 2 |
| C89×#2541 | 2 |
| #9405 | 89 |