Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
694 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 694 conjugacy classes of subgroups — too many to draw. Only its 107 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. C2×#19098361 | C2 | semidirect |
| 4. #23761526 | C2 | semidirect |
| 242. C79 | #13095 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23767024 | 2 |
| C2×#19098361 | 2 |
| #23763328 | 2 |
| #23761526 | 2 |
| C2×#413×C79 | 2 |
| #13095 | 79 |