Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
542 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 105 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. #26023437 | C2 | semidirect |
| 5. C2×#19151339 | C2 | semidirect |
| 6. #26018134 | C2 | semidirect |
| 7. C89×#1295 | C2 | semidirect |
| 11. #19151963 | C4 | semidirect |
| 224. #1295 | D89 | semidirect |
| 225. C89 | #9002 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151963 | 2 |
| #26023437 | 2 |
| #26021076 | 2 |
| #26021075 | 2 |
| C2×#19151339 | 2 |
| #26018134 | 2 |
| C89×#1295 | 2 |
| #9002 | 89 |