Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
452 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 4. #23761994 | C2 | semidirect |
| 5. #23761911 | C2 | semidirect |
| 6. #23761271 | C2 | semidirect |
| 7. C79×#1300 | C2 | semidirect |
| 11. #19098859 | C4 | semidirect |
| 12. #19098854 | C4 | semidirect |
| 13. #19098774 | C4 | semidirect |
| 14. #19098769 | C4 | semidirect |
| 200. #1300 | D79 | semidirect |
| 202. C79 | #9159 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773563 | 2 |
| #23772415 | 2 |
| #23763211 | 2 |
| #23761994 | 2 |
| #23761911 | 2 |
| #23761271 | 2 |
| C79×#1300 | 2 |
| #9159 | 79 |