Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
776 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 776 conjugacy classes of subgroups — too many to draw. Only its 123 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. #26018272 | C2 | direct (N × H) |
| 5. C23×Dic178 | C4 | semidirect |
| 10. #19151510 | C4 | semidirect |
| 13. C2×#15667919 | C4 | semidirect |
| 24. C22×Dic178 | C2×C4 | semidirect |
| 36. #15667919 | C2×C4 | semidirect |
| 203. C2×C89 | #1351 | semidirect |
| 211. C89 | C2×#1351 | semidirect |
| 409. C2 | #26018272 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151510 | 2 |
| C2×#19151322 | 2 |
| #26018272 | 2 |
| C2×#342×C89 | 2 |
| C2×#1351 | 89 |