Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
236 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 83 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. #26022084 | C2 | semidirect |
| 2. #26022083 | C2 | semidirect |
| 4. #26018315 | C2 | semidirect |
| 5. #26018208 | C2 | semidirect |
| 6. #26018171 | C2 | semidirect |
| 7. C89×D4⋊C16 | C2 | semidirect |
| 93. #10623494 | M32 | semidirect |
| 119. D4⋊C16 | D89 | semidirect |
| 121. C89 | #12064 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022084 | 2 |
| #26022083 | 2 |
| C8×#13083559 | 2 |
| #26018315 | 2 |
| #26018208 | 2 |
| #26018171 | 2 |
| C89×D4⋊C16 | 2 |
| #12064 | 89 |