Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
584 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 127 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×C4×Dic178 | C4 | semidirect |
| 9. #19151503 | C4 | semidirect |
| 13. #19151463 | C4 | semidirect |
| 17. C42×Dic89 | C4 | semidirect |
| 18. #19151392 | C4 | direct (N × H) |
| 66. C2×Dic178 | C42 | semidirect |
| 87. C4×Dic89 | C42 | semidirect |
| 186. C4×C89 | #354 | semidirect |
| 205. C89 | C4×#354 | semidirect |
| 391. C4 | #19151392 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#15667999 | 2 |
| C2×#19151392 | 2 |
| C4×#15667927 | 2 |
| #26018376 | 2 |
| C4×#99×C89 | 2 |
| C4×#354 | 89 |