Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
736 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 736 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 |
|---|---|---|
| 2. #23764369 | C2 | semidirect |
| 4. C2×#19098304 | C2 | semidirect |
| 8. #19099313 | C4 | semidirect |
| 172. C79 | #8507 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19099313 | 2 |
| #23764369 | 2 |
| #23764217 | 2 |
| C2×#19098304 | 2 |
| C2×#329×C79 | 2 |
| #8507 | 79 |