Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
408 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 71 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. #23765085 | C2 | semidirect |
| 3. #23761559 | C2 | semidirect |
| 4. #23761556 | C2 | semidirect |
| 5. C79×#2126 | C2 | semidirect |
| 8. #19099113 | C4 | semidirect |
| 9. #19098958 | C4 | semidirect |
| 12. #19098953 | C4 | semidirect |
| 16. C2×#14579072 | C4 | semidirect |
| 175. #2126 | D79 | semidirect |
| 178. C79 | #13577 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773845 | 2 |
| #23765085 | 2 |
| #23761559 | 2 |
| #23761556 | 2 |
| C79×#2126 | 2 |
| #13577 | 79 |