Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
922 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 922 conjugacy classes of subgroups — too many to draw. Only its 187 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. #23773978 | C2 | semidirect |
| 2. #23773829 | C2 | semidirect |
| 3. #23773827 | C2 | semidirect |
| 4. #23763016 | C2 | semidirect |
| 5. #23763014 | C2 | semidirect |
| 6. #23763006 | C2 | semidirect |
| 7. #23762991 | C2 | semidirect |
| 8. C82×D79 | C2 | semidirect |
| 9. C79×#1709 | C2 | semidirect |
| 85. C8×D79 | D8 | semidirect |
| 124. C79⋊C8 | #135 | semidirect |
| 150. #1709 | D79 | semidirect |
| 153. C79 | #19603 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773978 | 2 |
| #23773829 | 2 |
| #23773827 | 2 |
| #23763016 | 2 |
| #23763014 | 2 |
| #23763006 | 2 |
| #23762991 | 2 |
| C82×D79 | 2 |
| C79×#1709 | 2 |
| #19603 | 79 |