Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
568 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 97 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. #26033386 | C2 | semidirect |
| 2. #26030733 | C2 | semidirect |
| 3. #26021989 | C2 | semidirect |
| 4. #26021968 | C2 | semidirect |
| 5. #26021151 | C2 | semidirect |
| 6. #26018339 | C2 | semidirect |
| 7. C2×#509×C89 | C2 | semidirect |
| 58. C2×#13083549 | D4 | semidirect |
| 71. C2×Q16×C89 | D4 | semidirect |
| 79. C2×D8×C89 | D4 | semidirect |
| 84. M32×C89 | D4 | semidirect |
| 219. C2×#509 | D89 | semidirect |
| 225. C89 | #13334 | semidirect |
| 265. C2×Q16 | C22⋊D89 | semidirect |
| 277. C2×D8 | C22⋊D89 | semidirect |
| 295. M32 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033386 | 2 |
| #26030733 | 2 |
| #26021989 | 2 |
| #26021968 | 2 |
| #26021151 | 2 |
| #26018339 | 2 |
| C2×#509×C89 | 2 |
| #13334 | 89 |