Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
332 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 67 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. #26018426 | C2 | semidirect |
| 4. #26018411 | C2 | semidirect |
| 6. #19152210 | C4 | semidirect |
| 8. #19151970 | C4 | semidirect |
| 9. #19151962 | C4 | semidirect |
| 15. #19151659 | C4 | semidirect |
| 28. #15668012 | C2×C4 | semidirect |
| 30. #15668004 | C2×C4 | semidirect |
| 42. #15667923 | C2×C4 | semidirect |
| 43. C4×#10623494 | C2×C4 | semidirect |
| 158. C89 | #13607 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031324 | 2 |
| #26021944 | 2 |
| #26018426 | 2 |
| #26018411 | 2 |
| C89×#2127 | 2 |
| #13607 | 89 |