Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
340 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 5. C2×#14579095 | C4 | semidirect |
| 6. C2×#14579093 | C4 | semidirect |
| 10. #19098320 | C4 | semidirect |
| 14. #349×C79 | C4 | semidirect |
| 148. C79 | #7254 | semidirect |
| 156. #349 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23763433 | 2 |
| C2×#19098320 | 2 |
| C2×#349×C79 | 2 |
| #7254 | 79 |