Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
686 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 686 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 3. #26021228 | C2 | semidirect |
| 4. #26018750 | C2 | semidirect |
| 6. #26018084 | C2 | semidirect |
| 7. C89×#1303 | C2 | semidirect |
| 13. #19151889 | C4 | semidirect |
| 14. #19151804 | C4 | semidirect |
| 33. #15668012 | C2×C4 | semidirect |
| 34. #15668012 | C2×C4 | semidirect |
| 69. C4⋊C8×C89 | C2×C4 | semidirect |
| 112. C4×Dic89 | SD16 | semidirect |
| 209. #1303 | D89 | semidirect |
| 211. C89 | #9231 | semidirect |
| 268. C4⋊C8 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030261 | 2 |
| C4×#15667974 | 2 |
| #26021228 | 2 |
| #26018750 | 2 |
| #26018676 | 2 |
| #26018084 | 2 |
| C89×#1303 | 2 |
| #9231 | 89 |