Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
594 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 3. #26021232 | C2 | semidirect |
| 5. #26018815 | C2 | semidirect |
| 6. #26018080 | C2 | semidirect |
| 7. C89×#1286 | C2 | semidirect |
| 11. #19151971 | C4 | semidirect |
| 12. #19151945 | C4 | semidirect |
| 32. #15668012 | C2×C4 | semidirect |
| 33. #15668012 | C2×C4 | semidirect |
| 64. C4×C8×C89 | C2×C4 | semidirect |
| 103. C4×Dic89 | SD16 | semidirect |
| 200. #1286 | D89 | semidirect |
| 202. C89 | #9295 | semidirect |
| 257. C4×C8 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031195 | 2 |
| #26022975 | 2 |
| #26021232 | 2 |
| #26018921 | 2 |
| #26018815 | 2 |
| #26018080 | 2 |
| C89×#1286 | 2 |
| #9295 | 89 |