Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1318 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 1318 conjugacy classes of subgroups — too many to draw. Only its 195 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. C2×#19099175 | C2 | semidirect |
| 3. #23764546 | C2 | semidirect |
| 4. #23764482 | C2 | semidirect |
| 5. #23763758 | C2 | semidirect |
| 6. #23763712 | C2 | semidirect |
| 7. #23763471 | C2 | semidirect |
| 11. C2×#14579161 | C22 | semidirect |
| 13. C2×#14579153 | C22 | semidirect |
| 16. C2×C4×Dic158 | C22 | semidirect |
| 18. C2×#14579084 | C22 | semidirect |
| 21. #19098325 | C22 | semidirect |
| 22. #19098318 | C22 | semidirect |
| 23. #19098318 | C22 | semidirect |
| 195. C79 | #23942 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19099175 | 2 |
| C2×#19098714 | 2 |
| #23764546 | 2 |
| #23764482 | 2 |
| #23763758 | 2 |
| #23763712 | 2 |
| #23763471 | 2 |
| C79×#2309 | 2 |
| #23942 | 79 |