Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
684 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 131 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. #26018823 | C2 | semidirect |
| 4. #26018119 | C2 | semidirect |
| 8. #19151534 | C4 | semidirect |
| 10. #19151510 | C4 | semidirect |
| 21. C22×Dic178 | C2×C4 | semidirect |
| 26. C2×C4⋊Dic89 | C2×C4 | semidirect |
| 36. #15667919 | C2×C4 | semidirect |
| 198. C89 | #9199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26026057 | 2 |
| #26018823 | 2 |
| C2×#19151322 | 2 |
| #26018119 | 2 |
| C89×#2315 | 2 |
| #9199 | 89 |