Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
464 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 95 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. #23761956 | C2 | semidirect |
| 3. #23761930 | C2 | semidirect |
| 4. #23761761 | C2 | semidirect |
| 5. #23761309 | C2 | semidirect |
| 6. #23761276 | C2 | semidirect |
| 7. C79×#2978 | C2 | semidirect |
| 9. #19098891 | C4 | semidirect |
| 11. #19098874 | C4 | semidirect |
| 14. #19098713 | C4 | semidirect |
| 16. #19098696 | C4 | semidirect |
| 227. #2978 | D79 | semidirect |
| 233. C79 | #9332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774210 | 2 |
| #23761956 | 2 |
| #23761930 | 2 |
| #23761761 | 2 |
| #23761309 | 2 |
| #23761276 | 2 |
| C79×#2978 | 2 |
| #9332 | 79 |