Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
728 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 179 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. #23774118 | C2 | semidirect |
| 3. #23773794 | C2 | semidirect |
| 4. #23773781 | C2 | semidirect |
| 5. #23763053 | C2 | semidirect |
| 6. #23763046 | C2 | semidirect |
| 7. #23763039 | C2 | semidirect |
| 8. #23763012 | C2 | semidirect |
| 9. C79×#1455 | C2 | semidirect |
| 167. #1455 | D79 | semidirect |
| 168. C79 | #19754 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774138 | 2 |
| #23774118 | 2 |
| #23773794 | 2 |
| #23773781 | 2 |
| #23763053 | 2 |
| #23763046 | 2 |
| #23763039 | 2 |
| #23763012 | 2 |
| C79×#1455 | 2 |
| #19754 | 79 |