Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
492 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 109 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. #26023000 | C2 | semidirect |
| 4. #26018932 | C2 | semidirect |
| 6. #26018111 | C2 | semidirect |
| 7. C89×#1274 | C2 | semidirect |
| 10. #19151971 | C4 | semidirect |
| 11. #19151949 | C4 | semidirect |
| 108. C42×C89 | SD16 | semidirect |
| 189. #1274 | D89 | semidirect |
| 190. C89 | #9301 | semidirect |
| 291. C42 | #13083563 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031179 | 2 |
| #26023000 | 2 |
| #26021084 | 2 |
| #26018932 | 2 |
| #26018813 | 2 |
| #26018111 | 2 |
| C89×#1274 | 2 |
| #9301 | 89 |