Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
696 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 143 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×#19152027 | C2 | semidirect |
| 2. #26032010 | C2 | semidirect |
| 3. #26022335 | C2 | semidirect |
| 4. #26022289 | C2 | semidirect |
| 5. #26022172 | C2 | semidirect |
| 6. C4×Dic712 | C2 | semidirect |
| 7. C16×D356 | C2 | semidirect |
| 8. C89×#2246 | C2 | semidirect |
| 41. Dic712 | D4 | semidirect |
| 122. C4×C89 | #508 | semidirect |
| 136. #2246 | D89 | semidirect |
| 142. C89 | #33853 | semidirect |
| 259. C4 | #19152027 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152027 | 2 |
| #26032010 | 2 |
| #26022335 | 2 |
| #26022289 | 2 |
| #26022172 | 2 |
| C4×Dic712 | 2 |
| C16×D356 | 2 |
| C89×#2246 | 2 |
| #33853 | 89 |