Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
486 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 1. #26026567 | C2 | semidirect |
| 4. #26018275 | C2 | semidirect |
| 5. #26018272 | C2 | semidirect |
| 6. #26018200 | C2 | semidirect |
| 114. C22⋊C4×C89 | SD16 | semidirect |
| 211. C89 | #12176 | semidirect |
| 317. C22⋊C4 | #13083562 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26026567 | 2 |
| #26019272 | 2 |
| #26019204 | 2 |
| #26018275 | 2 |
| #26018272 | 2 |
| #26018200 | 2 |
| C89×#2044 | 2 |
| #12176 | 89 |