Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
304 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 1. #23765160 | C2 | semidirect |
| 5. #23764191 | C2 | semidirect |
| 6. #23761495 | C2 | semidirect |
| 7. C79×#2155 | C2 | semidirect |
| 137. #2155 | D79 | semidirect |
| 144. C79 | #13468 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765160 | 2 |
| #23765129 | 2 |
| C2×#19098369 | 2 |
| #23764296 | 2 |
| #23764191 | 2 |
| #23761495 | 2 |
| C79×#2155 | 2 |
| #13468 | 79 |