Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
458 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 113 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. #23763571 | C2 | semidirect |
| 3. #23762085 | C2 | semidirect |
| 6. #23761693 | C2 | semidirect |
| 7. C79×#1548 | C2 | semidirect |
| 153. #1548 | D79 | semidirect |
| 157. C79 | #9774 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098911 | 2 |
| #23763571 | 2 |
| #23762085 | 2 |
| #23762069 | 2 |
| #23762067 | 2 |
| #23761693 | 2 |
| C79×#1548 | 2 |
| #9774 | 79 |