Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
452 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 2. #23772572 | C2 | semidirect |
| 3. #23764232 | C2 | semidirect |
| 4. #23761884 | C2 | semidirect |
| 5. #23761868 | C2 | semidirect |
| 6. #23761290 | C2 | semidirect |
| 7. C79×#1300 | C2 | semidirect |
| 10. #19098972 | C4 | semidirect |
| 11. #19098952 | C4 | semidirect |
| 12. #19098928 | C4 | semidirect |
| 13. #19098923 | C4 | semidirect |
| 221. #1300 | D79 | semidirect |
| 223. C79 | #8997 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773995 | 2 |
| #23772572 | 2 |
| #23764232 | 2 |
| #23761884 | 2 |
| #23761868 | 2 |
| #23761290 | 2 |
| C79×#1300 | 2 |
| #8997 | 79 |