Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
456 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 456 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. #23772475 | C2 | semidirect |
| 3. #23761907 | C2 | semidirect |
| 4. #23761907 | C2 | semidirect |
| 5. #23761870 | C2 | semidirect |
| 6. #23761262 | C2 | semidirect |
| 7. C79×#1274 | C2 | semidirect |
| 10. #19098940 | C4 | semidirect |
| 11. #19098936 | C4 | semidirect |
| 12. #19098914 | C4 | semidirect |
| 13. #19098910 | C4 | semidirect |
| 185. #1274 | D79 | semidirect |
| 186. C79 | #9281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774335 | 2 |
| #23772475 | 2 |
| #23761907 | 2 |
| #23761870 | 2 |
| #23761262 | 2 |
| C79×#1274 | 2 |
| #9281 | 79 |