Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
378 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 2. #23765160 | C2 | semidirect |
| 4. #23763523 | C2 | semidirect |
| 5. #23761512 | C2 | semidirect |
| 6. #23761495 | C2 | semidirect |
| 10. #19098685 | C4 | semidirect |
| 148. C79 | #12830 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772317 | 2 |
| #23765160 | 2 |
| C2×#19098370 | 2 |
| #23763523 | 2 |
| #23761512 | 2 |
| #23761495 | 2 |
| C79×#2145 | 2 |
| #12830 | 79 |