Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
566 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 3. #23761963 | C2 | semidirect |
| 4. #23761900 | C2 | semidirect |
| 6. #23761301 | C2 | semidirect |
| 7. C79×#1286 | C2 | semidirect |
| 12. #19098854 | C4 | semidirect |
| 13. #19098844 | C4 | semidirect |
| 32. #14579161 | C2×C4 | semidirect |
| 33. #14579161 | C2×C4 | semidirect |
| 67. C4⋊C8×C79 | C2×C4 | semidirect |
| 202. #1286 | D79 | semidirect |
| 203. C79 | #9175 | semidirect |
| 256. C4⋊C8 | C4×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773199 | 2 |
| #23766308 | 2 |
| #23761963 | 2 |
| #23761900 | 2 |
| #23761790 | 2 |
| #23761301 | 2 |
| C79×#1286 | 2 |
| #9175 | 79 |