Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
456 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 456 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 |
|---|---|---|
| 2. #26020277 | C2 | semidirect |
| 4. #26018159 | C2 | semidirect |
| 5. C89×#1810 | C2 | semidirect |
| 6. C2×#15668018 | C4 | semidirect |
| 13. #19151624 | C4 | semidirect |
| 14. #19151564 | C4 | semidirect |
| 16. #19151553 | C4 | semidirect |
| 186. #1810 | D89 | semidirect |
| 190. C89 | #8629 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028946 | 2 |
| #26020277 | 2 |
| #26018796 | 2 |
| #26018159 | 2 |
| C89×#1810 | 2 |
| #8629 | 89 |