Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
460 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 119 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 |
|---|---|---|
| 1. C2×#19151420 | C2 | semidirect |
| 4. #26021005 | C2 | semidirect |
| 5. #26018359 | C2 | semidirect |
| 6. #26018332 | C2 | semidirect |
| 15. #19151399 | C4 | semidirect |
| 31. C2×#13083549 | C2×C4 | semidirect |
| 34. #15667946 | C2×C4 | semidirect |
| 152. C89 | #12956 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151420 | 2 |
| C2×#19151411 | 2 |
| #26021968 | 2 |
| #26021005 | 2 |
| #26018359 | 2 |
| #26018332 | 2 |
| C2×#442×C89 | 2 |
| #12956 | 89 |