Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
422 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 422 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 |
|---|---|---|
| 3. #23761912 | C2 | semidirect |
| 5. #23761261 | C2 | semidirect |
| 6. #23761228 | C2 | semidirect |
| 7. C79×#1497 | C2 | semidirect |
| 9. #19098966 | C4 | semidirect |
| 10. #19098959 | C4 | semidirect |
| 11. #19098911 | C4 | semidirect |
| 12. #19098911 | C4 | semidirect |
| 173. #1497 | D79 | semidirect |
| 176. C79 | #9279 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774536 | 2 |
| #23772475 | 2 |
| #23761912 | 2 |
| #23761909 | 2 |
| #23761261 | 2 |
| #23761228 | 2 |
| C79×#1497 | 2 |
| #9279 | 79 |