Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
538 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 538 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 |
|---|---|---|
| 1. C2×#19151710 | C2 | semidirect |
| 2. C2×#19151411 | C2 | semidirect |
| 3. C2×#19151408 | C2 | semidirect |
| 4. #26021146 | C2 | semidirect |
| 5. #26018351 | C2 | semidirect |
| 6. #26018331 | C2 | semidirect |
| 24. C2×SD32×C89 | C4 | semidirect |
| 25. C2×D16×C89 | C4 | semidirect |
| 53. C2×Q16×C89 | C2×C4 | semidirect |
| 59. C2×D8×C89 | C2×C4 | semidirect |
| 67. C2×C16×C89 | C2×C4 | semidirect |
| 186. C89 | #13037 | semidirect |
| 192. C2×SD32 | Dic89 | semidirect |
| 193. C2×D16 | Dic89 | semidirect |
| 213. C2×Q16 | C2×Dic89 | semidirect |
| 219. C2×D8 | C2×Dic89 | semidirect |
| 237. C2×C16 | C2×Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151710 | 2 |
| C2×#19151411 | 2 |
| C2×#19151408 | 2 |
| #26021146 | 2 |
| #26018351 | 2 |
| #26018331 | 2 |
| C2×#509×C89 | 2 |
| #13037 | 89 |