Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
544 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 7. C2×#15667977 | C4 | semidirect |
| 10. #19151504 | C4 | semidirect |
| 12. #19151463 | C4 | semidirect |
| 15. C42×Dic89 | C4 | semidirect |
| 55. C2×Dic178 | C4⋊C4 | semidirect |
| 80. C4×Dic89 | C4⋊C4 | semidirect |
| 161. Dic89 | #354 | semidirect |
| 175. C89 | #12798 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022799 | 2 |
| C2×#19151392 | 2 |
| #26020238 | 2 |
| #26018377 | 2 |
| C89×#1393 | 2 |
| #12798 | 89 |