Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
390 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 75 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. #26018422 | C2 | direct (N × H) |
| 5. C2×#15668004 | C4 | semidirect |
| 8. #19151962 | C4 | semidirect |
| 13. C2×#15667923 | C4 | semidirect |
| 23. #15668004 | C2×C4 | semidirect |
| 34. #15667923 | C2×C4 | semidirect |
| 148. C2×C89 | #1412 | semidirect |
| 154. C89 | C2×#1412 | semidirect |
| 297. C2 | #26018422 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151962 | 2 |
| C2×#19151391 | 2 |
| #26018422 | 2 |
| C2×#353×C89 | 2 |
| C2×#1412 | 89 |