Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
586 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 586 conjugacy classes of subgroups — too many to draw. Only its 101 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×#19152034 | C2 | semidirect |
| 2. #26030733 | C2 | semidirect |
| 3. C2×#19151411 | C2 | semidirect |
| 4. C2×#19151406 | C2 | semidirect |
| 5. #26021163 | C2 | semidirect |
| 6. #26018340 | C2 | semidirect |
| 7. C22×D16×C89 | C2 | semidirect |
| 53. #15667952 | D4 | semidirect |
| 74. C2×D8×C89 | D4 | semidirect |
| 79. C2×C16×C89 | D4 | semidirect |
| 208. C22×D16 | D89 | semidirect |
| 214. C89 | #13336 | semidirect |
| 263. C2×D8 | C22⋊D89 | semidirect |
| 280. C2×C16 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152034 | 2 |
| #26030733 | 2 |
| C2×#19151411 | 2 |
| C2×#19151406 | 2 |
| #26021163 | 2 |
| #26018340 | 2 |
| C22×D16×C89 | 2 |
| #13336 | 89 |