Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
444 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 105 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×#19151420 | C2 | semidirect |
| 3. C2×#19151412 | C2 | semidirect |
| 4. C2×#19151375 | C2 | semidirect |
| 5. #26021146 | C2 | semidirect |
| 6. #26021126 | C2 | semidirect |
| 7. C2×#360×C89 | C2 | semidirect |
| 11. C2×#15667955 | C4 | semidirect |
| 12. C2×#15667953 | C4 | semidirect |
| 86. #13083549 | C22⋊C4 | semidirect |
| 176. C2×#360 | D89 | semidirect |
| 180. C89 | #13249 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152033 | 2 |
| C2×#19151420 | 2 |
| C2×#19151412 | 2 |
| C2×#19151375 | 2 |
| #26021146 | 2 |
| #26021126 | 2 |
| C2×#360×C89 | 2 |
| #13249 | 89 |