Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
606 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 606 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. #26021236 | C2 | semidirect |
| 5. C2×#19151334 | C2 | semidirect |
| 6. #26018098 | C2 | semidirect |
| 7. C89×#1294 | C2 | semidirect |
| 12. #19151917 | C4 | semidirect |
| 15. #19151739 | C4 | semidirect |
| 31. C22×Dic178 | C2×C4 | semidirect |
| 47. C2×C4⋊Dic89 | C2×C4 | semidirect |
| 74. C22⋊C8×C89 | C2×C4 | semidirect |
| 115. C22⋊Dic89 | SD16 | semidirect |
| 256. #1294 | D89 | semidirect |
| 258. C89 | #9275 | semidirect |
| 322. C22⋊C8 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031010 | 2 |
| #26023299 | 2 |
| #26021236 | 2 |
| #26018819 | 2 |
| C2×#19151334 | 2 |
| #26018098 | 2 |
| C89×#1294 | 2 |
| #9275 | 89 |