Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
726 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 111 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. #26018771 | C2 | semidirect |
| 4. #26018138 | C2 | semidirect |
| 8. #19151523 | C4 | semidirect |
| 9. #19151510 | C4 | semidirect |
| 21. C22×Dic178 | C2×C4 | semidirect |
| 25. C2×C4⋊Dic89 | C2×C4 | semidirect |
| 36. #15667919 | C2×C4 | semidirect |
| 174. C89 | #9407 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26025410 | 2 |
| #26018771 | 2 |
| #26018579 | 2 |
| #26018138 | 2 |
| C89×#2273 | 2 |
| #9407 | 89 |