Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
318 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 16. #19098311 | C4 | semidirect |
| 17. #19098311 | C4 | semidirect |
| 18. #19098310 | C4 | semidirect |
| 19. #19098310 | C4 | semidirect |
| 160. C79 | #9591 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23764343 | 2 |
| #23764173 | 2 |
| #23762055 | 2 |
| #23761854 | 2 |
| #23761690 | 2 |
| #23761241 | 2 |
| C79×#1303 | 2 |
| #9591 | 79 |