Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
434 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 111 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×#19098380 | C2 | semidirect |
| 5. #23765121 | C2 | semidirect |
| 6. #23763524 | C2 | semidirect |
| 7. C79×#2110 | C2 | semidirect |
| 13. #19098947 | C4 | semidirect |
| 14. #19098943 | C4 | semidirect |
| 174. #2110 | D79 | semidirect |
| 176. C79 | #13216 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773894 | 2 |
| C2×#19098380 | 2 |
| #23765137 | 2 |
| #23765129 | 2 |
| #23765121 | 2 |
| #23763524 | 2 |
| C79×#2110 | 2 |
| #13216 | 79 |