Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
334 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 12. #19098590 | C4 | semidirect |
| 13. #19098590 | C4 | semidirect |
| 18. C4×#11929608 | C4 | semidirect |
| 19. C2×#14579072 | C4 | semidirect |
| 174. C79 | #12865 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772051 | 2 |
| #23763504 | 2 |
| #23761530 | 2 |
| #23761528 | 2 |
| #23761522 | 2 |
| #23761520 | 2 |
| C79×#1827 | 2 |
| #12865 | 79 |