Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
414 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 414 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. #23764381 | C2 | semidirect |
| 5. #23761872 | C2 | semidirect |
| 6. #23761290 | C2 | semidirect |
| 7. C79×#1300 | C2 | semidirect |
| 10. #19098972 | C4 | semidirect |
| 11. #19098957 | C4 | semidirect |
| 12. #19098932 | C4 | semidirect |
| 13. #19098923 | C4 | semidirect |
| 204. #1300 | D79 | semidirect |
| 206. C79 | #8998 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774006 | 2 |
| #23772572 | 2 |
| #23764381 | 2 |
| #23761884 | 2 |
| #23761872 | 2 |
| #23761290 | 2 |
| C79×#1300 | 2 |
| #8998 | 79 |