Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
542 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 542 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. #26023438 | C2 | semidirect |
| 4. #26018134 | C2 | semidirect |
| 5. C2×#330×C89 | C2 | semidirect |
| 8. #19151964 | C4 | semidirect |
| 139. C2×#330 | D89 | semidirect |
| 141. C89 | #9002 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151964 | 2 |
| #26023438 | 2 |
| #26021076 | 2 |
| #26018134 | 2 |
| C2×#330×C89 | 2 |
| #9002 | 89 |