Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
382 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 151 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. #26021856 | C2 | semidirect |
| 4. #26018342 | C2 | semidirect |
| 7. C2×#15667952 | C4 | semidirect |
| 9. C22×#13083549 | C4 | semidirect |
| 18. #349×C89 | C4 | semidirect |
| 107. C89 | #12617 | semidirect |
| 118. #349 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152015 | 2 |
| #26021856 | 2 |
| #26020052 | 2 |
| #26018342 | 2 |
| C89×#2115 | 2 |
| #12617 | 89 |