Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
644 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 93 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. #23763334 | C2 | semidirect |
| 4. #23763323 | C2 | semidirect |
| 6. #23761276 | C2 | semidirect |
| 7. C79×#1305 | C2 | semidirect |
| 12. #19098721 | C4 | semidirect |
| 14. #19098704 | C4 | semidirect |
| 256. #1305 | D79 | semidirect |
| 258. C79 | #9519 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772637 | 2 |
| #23772450 | 2 |
| #23763334 | 2 |
| #23763323 | 2 |
| #23761941 | 2 |
| #23761276 | 2 |
| C79×#1305 | 2 |
| #9519 | 79 |