Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
874 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 874 conjugacy classes of subgroups — too many to draw. Only its 127 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. #23763162 | C2 | semidirect |
| 3. #23761220 | C2 | semidirect |
| 4. C79×#1749 | C2 | semidirect |
| 15. #19098318 | C22 | semidirect |
| 19. #336×C79 | C22 | semidirect |
| 195. #1749 | D79 | semidirect |
| 197. C79 | #7626 | semidirect |
| 212. #336 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098465 | 2 |
| #23763162 | 2 |
| #23761220 | 2 |
| C79×#1749 | 2 |
| #7626 | 79 |