Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
412 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 97 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. #23762191 | C2 | semidirect |
| 5. #23761232 | C2 | semidirect |
| 6. #23761232 | C2 | semidirect |
| 7. C79×#1574 | C2 | semidirect |
| 20. #19098311 | C4 | semidirect |
| 21. #19098311 | C4 | semidirect |
| 22. #19098306 | C4 | semidirect |
| 23. #19098306 | C4 | semidirect |
| 166. #1574 | D79 | semidirect |
| 170. C79 | #8935 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772466 | 2 |
| #23764227 | 2 |
| #23762191 | 2 |
| #23762060 | 2 |
| #23761232 | 2 |
| C79×#1574 | 2 |
| #8935 | 79 |