Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
814 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 814 conjugacy classes of subgroups — too many to draw. Only its 159 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 |
|---|---|---|
| 1. #23774139 | C2 | semidirect |
| 2. #23774139 | C2 | semidirect |
| 3. #23773858 | C2 | semidirect |
| 4. #23773795 | C2 | semidirect |
| 5. #23763066 | C2 | semidirect |
| 6. #23763058 | C2 | semidirect |
| 7. #23763042 | C2 | semidirect |
| 8. #23763007 | C2 | semidirect |
| 9. #23763002 | C2 | semidirect |
| 10. #23761704 | C2 | semidirect |
| 11. C79×#1716 | C2 | semidirect |
| 193. #1716 | D79 | semidirect |
| 197. C79 | #19750 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774139 | 2 |
| #23773858 | 2 |
| #23773795 | 2 |
| #23763066 | 2 |
| #23763058 | 2 |
| #23763042 | 2 |
| #23763007 | 2 |
| #23763002 | 2 |
| #23761704 | 2 |
| C79×#1716 | 2 |
| #19750 | 79 |