Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
452 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 452 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. C2×#14579094 | C4 | semidirect |
| 17. C2×#14579092 | C4 | semidirect |
| 19. C2×#14579084 | C4 | semidirect |
| 20. C2×#14579084 | C4 | semidirect |
| 221. C79 | #9240 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098904 | 2 |
| #23772058 | 2 |
| #23761919 | 2 |
| #23761765 | 2 |
| #23761276 | 2 |
| #23761248 | 2 |
| C79×#1826 | 2 |
| #9240 | 79 |