Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
726 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 211 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 |
|---|---|---|
| 2. #26021058 | C2 | semidirect |
| 3. #26020412 | C2 | semidirect |
| 4. C2×C82×C89 | C2 | semidirect |
| 8. #19151975 | C4 | semidirect |
| 53. C2×C8×C89 | D8 | semidirect |
| 79. C8×C89 | #102 | semidirect |
| 105. C2×C82 | D89 | semidirect |
| 106. C89 | #9824 | semidirect |
| 153. C2×C8 | D712 | semidirect |
| 181. C8 | #15667934 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151975 | 2 |
| #26021058 | 2 |
| #26020412 | 2 |
| C2×C82×C89 | 2 |
| #9824 | 89 |