Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
548 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 105 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. #23766371 | C2 | semidirect |
| 3. #23761961 | C2 | semidirect |
| 4. #23761894 | C2 | semidirect |
| 5. #23761792 | C2 | semidirect |
| 6. #23761260 | C2 | semidirect |
| 7. C79×#1303 | C2 | semidirect |
| 12. #19098769 | C4 | semidirect |
| 13. #19098759 | C4 | semidirect |
| 215. #1303 | D79 | semidirect |
| 217. C79 | #9181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772866 | 2 |
| #23766371 | 2 |
| #23761961 | 2 |
| #23761894 | 2 |
| #23761792 | 2 |
| #23761260 | 2 |
| C79×#1303 | 2 |
| #9181 | 79 |