Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
306 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 17. #499×C89 | C4 | semidirect |
| 18. #498×C89 | C4 | semidirect |
| 28. #15667952 | Q8 | semidirect |
| 30. C2×#13083549 | Q8 | semidirect |
| 131. C89 | #13291 | semidirect |
| 136. #499 | Dic89 | semidirect |
| 137. #498 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021857 | 2 |
| #26020376 | 2 |
| #26018368 | 2 |
| #26018359 | 2 |
| #26018353 | 2 |
| #26018350 | 2 |
| C89×#3163 | 2 |
| #13291 | 89 |