Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
510 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 107 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. #23763176 | C2 | semidirect |
| 3. #23761921 | C2 | semidirect |
| 5. #23761765 | C2 | semidirect |
| 7. C79×#1810 | C2 | semidirect |
| 8. C22×#11929613 | C4 | semidirect |
| 15. C2×#14579093 | C4 | semidirect |
| 16. C2×#14579086 | C4 | semidirect |
| 17. C2×#14579083 | C4 | semidirect |
| 217. #1810 | D79 | semidirect |
| 223. C79 | #9816 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098792 | 2 |
| #23763176 | 2 |
| #23761921 | 2 |
| #23761917 | 2 |
| #23761765 | 2 |
| #23761761 | 2 |
| C79×#1810 | 2 |
| #9816 | 79 |