Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
464 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 464 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 |
|---|---|---|
| 1. #23765011 | C2 | semidirect |
| 2. #23763425 | C2 | semidirect |
| 3. #23761409 | C2 | semidirect |
| 9. C22⋊(C79⋊C16) | C22 | semidirect |
| 10. #19098326 | C22 | semidirect |
| 11. C22×D8×C79 | C4 | semidirect |
| 16. #466×C79 | C4 | semidirect |
| 18. C2×#107×C79 | C4 | semidirect |
| 159. C79 | #11888 | semidirect |
| 160. C22×D8 | Dic79 | semidirect |
| 166. #466 | Dic79 | semidirect |
| 168. C2×#107 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765011 | 2 |
| #23763425 | 2 |
| #23761409 | 2 |
| C2×#466×C79 | 2 |
| #11888 | 79 |