Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
278 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 4. #19099330 | C4 | semidirect |
| 7. #19098537 | C4 | semidirect |
| 8. #19098358 | C4 | semidirect |
| 13. #333×C79 | C4 | semidirect |
| 125. C79 | #7482 | semidirect |
| 135. #333 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765065 | 2 |
| #23763784 | 2 |
| C79×#1560 | 2 |
| #7482 | 79 |