Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1026 conjugacy classes of subgroups; only the 255 normal subgroups are shown.
This group has 1026 conjugacy classes of subgroups — too many to draw. Only its 255 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. #23764199 | C2 | semidirect |
| 2. #23764015 | C2 | semidirect |
| 3. #23763698 | C2 | semidirect |
| 4. #23763310 | C2 | semidirect |
| 6. C22×#11929608 | C22 | semidirect |
| 7. C2×C4⋊(C79⋊C8) | C22 | semidirect |
| 10. C2×C22⋊(C79⋊C8) | C22 | semidirect |
| 11. C2×#14579072 | C22 | semidirect |
| 12. #19098318 | C22 | semidirect |
| 52. C24×C79 | M16 | semidirect |
| 140. C79 | #23309 | semidirect |
| 182. C24 | #11929608 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23764199 | 2 |
| #23764015 | 2 |
| #23763698 | 2 |
| #23763310 | 2 |
| C4×#120×C79 | 2 |
| #23309 | 79 |