Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
356 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 17. #19098309 | C4 | semidirect |
| 18. #19098309 | C4 | semidirect |
| 19. #19098309 | C4 | semidirect |
| 20. #19098309 | C4 | semidirect |
| 157. C79 | #8936 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23764378 | 2 |
| #23762188 | 2 |
| #23762065 | 2 |
| #23761232 | 2 |
| C79×#2986 | 2 |
| #8936 | 79 |