Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
430 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 119 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. #26022051 | C2 | semidirect |
| 3. #26018212 | C2 | semidirect |
| 4. C89×#1567 | C2 | semidirect |
| 15. C4×#13083549 | C22 | semidirect |
| 19. #335×C89 | C22 | semidirect |
| 58. D712 | M16 | semidirect |
| 133. #1567 | D89 | semidirect |
| 135. C89 | #11657 | semidirect |
| 150. #335 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D712 | 2 |
| #26022051 | 2 |
| #26018212 | 2 |
| C89×#1567 | 2 |
| #11657 | 89 |