Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
684 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 171 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 |
|---|---|---|
| 4. #23763075 | C2 | semidirect |
| 5. #23763047 | C2 | semidirect |
| 6. #23763032 | C2 | semidirect |
| 7. #23762996 | C2 | semidirect |
| 160. C79 | #19751 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774141 | 2 |
| #23773947 | 2 |
| #23773781 | 2 |
| #23763075 | 2 |
| #23763047 | 2 |
| #23763032 | 2 |
| #23762996 | 2 |
| #23761703 | 2 |
| C79×#3185 | 2 |
| #19751 | 79 |