Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
834 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 834 conjugacy classes of subgroups — too many to draw. Only its 179 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. C2×#19152031 | C2 | semidirect |
| 2. #26030681 | C2 | semidirect |
| 3. #26022514 | C2 | semidirect |
| 4. #26022509 | C2 | semidirect |
| 5. #26022502 | C2 | semidirect |
| 6. C4×C16×D89 | C2 | semidirect |
| 7. C89×#2247 | C2 | semidirect |
| 42. C16×D89 | D4 | semidirect |
| 107. C4×C89 | #508 | semidirect |
| 121. #2247 | D89 | semidirect |
| 124. C89 | #33713 | semidirect |
| 226. C4 | #19152031 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152031 | 2 |
| #26030681 | 2 |
| #26022514 | 2 |
| #26022509 | 2 |
| #26022502 | 2 |
| C4×C16×D89 | 2 |
| C89×#2247 | 2 |
| #33713 | 89 |