Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
422 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 422 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 |
|---|---|---|
| 3. #23761911 | C2 | semidirect |
| 5. #23761874 | C2 | semidirect |
| 6. #23761262 | C2 | semidirect |
| 7. C79×#1274 | C2 | semidirect |
| 10. #19098968 | C4 | semidirect |
| 11. #19098961 | C4 | semidirect |
| 12. #19098910 | C4 | semidirect |
| 13. #19098910 | C4 | semidirect |
| 175. #1274 | D79 | semidirect |
| 176. C79 | #9279 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774538 | 2 |
| #23772475 | 2 |
| #23761911 | 2 |
| #23761907 | 2 |
| #23761874 | 2 |
| #23761262 | 2 |
| C79×#1274 | 2 |
| #9279 | 79 |