Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
456 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 109 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×#19098979 | C2 | semidirect |
| 3. #23765135 | C2 | semidirect |
| 4. C2×#19098371 | C2 | semidirect |
| 5. #23763451 | C2 | semidirect |
| 6. #23761513 | C2 | semidirect |
| 7. C79×#1382 | C2 | semidirect |
| 16. #19098839 | C4 | semidirect |
| 17. #19098834 | C4 | semidirect |
| 187. #1382 | D79 | semidirect |
| 188. C79 | #13071 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098979 | 2 |
| #23773121 | 2 |
| #23765135 | 2 |
| C2×#19098371 | 2 |
| #23763451 | 2 |
| #23761513 | 2 |
| C79×#1382 | 2 |
| #13071 | 79 |