Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
536 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 21. #19151392 | C4 | semidirect |
| 76. C2×Dic178 | C4⋊C4 | semidirect |
| 109. C4×Dic89 | C4⋊C4 | semidirect |
| 237. C89 | #12965 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023361 | 2 |
| C2×#19151392 | 2 |
| #26020638 | 2 |
| #26020535 | 2 |
| #26020532 | 2 |
| #26018371 | 2 |
| C89×#1390 | 2 |
| #12965 | 89 |