Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
552 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 99 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×#19152041 | C2 | semidirect |
| 3. C2×#19151856 | C2 | semidirect |
| 4. C2×#19151409 | C2 | semidirect |
| 5. #26021973 | C2 | semidirect |
| 6. #26018358 | C2 | semidirect |
| 7. C2×#349×C89 | C2 | semidirect |
| 43. C2×Dic356 | D4 | semidirect |
| 62. #15667944 | D4 | semidirect |
| 78. M32×C89 | D4 | semidirect |
| 217. C2×#349 | D89 | semidirect |
| 219. C89 | #13317 | semidirect |
| 283. M32 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152041 | 2 |
| #26029861 | 2 |
| C2×#19151856 | 2 |
| C2×#19151409 | 2 |
| #26021973 | 2 |
| #26018358 | 2 |
| C2×#349×C89 | 2 |
| #13317 | 89 |