Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
456 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 89 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. #23772475 | C2 | semidirect |
| 3. #23761909 | C2 | semidirect |
| 4. #23761908 | C2 | semidirect |
| 5. #23761261 | C2 | semidirect |
| 6. #23761228 | C2 | semidirect |
| 7. C79×#1496 | C2 | semidirect |
| 9. #19098939 | C4 | semidirect |
| 10. #19098937 | C4 | semidirect |
| 11. #19098913 | C4 | semidirect |
| 12. #19098909 | C4 | semidirect |
| 183. #1496 | D79 | semidirect |
| 186. C79 | #9281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774333 | 2 |
| #23772475 | 2 |
| #23761909 | 2 |
| #23761908 | 2 |
| #23761261 | 2 |
| #23761228 | 2 |
| C79×#1496 | 2 |
| #9281 | 79 |