Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
538 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 538 conjugacy classes of subgroups — too many to draw. Only its 89 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. #26020352 | C2 | semidirect |
| 4. #26020327 | C2 | semidirect |
| 6. #26018161 | C2 | semidirect |
| 7. C89×#1284 | C2 | semidirect |
| 11. #19151917 | C4 | semidirect |
| 12. #19151912 | C4 | semidirect |
| 43. C2×C4⋊Dic89 | C2×C4 | semidirect |
| 44. C2×C4⋊Dic89 | C2×C4 | semidirect |
| 73. C22⋊C8×C89 | C2×C4 | semidirect |
| 238. #1284 | D89 | semidirect |
| 239. C89 | #9525 | semidirect |
| 301. C22⋊C8 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030193 | 2 |
| #26023017 | 2 |
| #26020352 | 2 |
| #26020327 | 2 |
| #26018780 | 2 |
| #26018161 | 2 |
| C89×#1284 | 2 |
| #9525 | 89 |