Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
496 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 3. #26021972 | C2 | semidirect |
| 4. #26021168 | C2 | semidirect |
| 5. #26018348 | C2 | semidirect |
| 6. #26018340 | C2 | semidirect |
| 24. C2×SD32×C89 | C4 | semidirect |
| 52. C2×Q16×C89 | C2×C4 | semidirect |
| 63. C2×C16×C89 | C2×C4 | semidirect |
| 168. C89 | #13019 | semidirect |
| 174. C2×SD32 | Dic89 | semidirect |
| 194. C2×Q16 | C2×Dic89 | semidirect |
| 215. C2×C16 | C2×Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029104 | 2 |
| C2×#19151411 | 2 |
| #26021972 | 2 |
| #26021168 | 2 |
| #26018348 | 2 |
| #26018340 | 2 |
| C22×SD32×C89 | 2 |
| #13019 | 89 |