Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1088 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 147 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. #26020162 | C2 | semidirect |
| 3. C2×#19151331 | C2 | semidirect |
| 4. #26018131 | C2 | semidirect |
| 5. C2×C4×C22⋊C4×C89 | C2 | semidirect |
| 6. C2×#15667986 | C4 | semidirect |
| 13. #19151458 | C4 | semidirect |
| 54. #95×C89 | D4 | semidirect |
| 207. C2×C4×C22⋊C4 | D89 | semidirect |
| 211. C89 | #9150 | semidirect |
| 260. #95 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028534 | 2 |
| #26020162 | 2 |
| C2×#19151331 | 2 |
| #26018131 | 2 |
| C2×C4×C22⋊C4×C89 | 2 |
| #9150 | 89 |