Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
694 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 694 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 2. #23765094 | C2 | semidirect |
| 3. #23765074 | C2 | semidirect |
| 5. #23763505 | C2 | semidirect |
| 6. #23763501 | C2 | semidirect |
| 15. #19099116 | C4 | semidirect |
| 18. C2×#14579148 | C4 | semidirect |
| 19. #19099040 | C4 | semidirect |
| 20. #19099038 | C4 | semidirect |
| 268. C79 | #12721 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23777295 | 2 |
| #23765094 | 2 |
| #23765074 | 2 |
| #23765050 | 2 |
| #23763505 | 2 |
| #23763501 | 2 |
| C79×#2122 | 2 |
| #12721 | 79 |