Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
458 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 458 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. C2×#19098378 | C2 | semidirect |
| 4. C2×#19098368 | C2 | semidirect |
| 6. #23761510 | C2 | semidirect |
| 7. C79×#1381 | C2 | semidirect |
| 17. #19098839 | C4 | semidirect |
| 177. #1381 | D79 | semidirect |
| 178. C79 | #13072 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098979 | 2 |
| C2×#19098839 | 2 |
| C2×#19098378 | 2 |
| C2×#19098368 | 2 |
| #23763461 | 2 |
| #23761510 | 2 |
| C79×#1381 | 2 |
| #13072 | 79 |