Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
444 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 111 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. C2×#19151410 | C2 | semidirect |
| 3. C2×#19151407 | C2 | semidirect |
| 4. C2×#19151375 | C2 | semidirect |
| 5. #26021143 | C2 | semidirect |
| 6. #26021126 | C2 | semidirect |
| 7. C2×#365×C89 | C2 | semidirect |
| 12. C2×#15667957 | C4 | semidirect |
| 13. C2×D1424 | C4 | semidirect |
| 111. C16×C89 | C22⋊C4 | semidirect |
| 174. C2×#365 | D89 | semidirect |
| 180. C89 | #13249 | semidirect |
| 284. C16 | #13083551 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152036 | 2 |
| C2×#19151410 | 2 |
| C2×#19151407 | 2 |
| C2×#19151375 | 2 |
| #26021143 | 2 |
| #26021126 | 2 |
| C2×#365×C89 | 2 |
| #13249 | 89 |