Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
656 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 211 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. #23763962 | C2 | semidirect |
| 4. #23763271 | C2 | semidirect |
| 6. #23763087 | C2 | semidirect |
| 7. C79×#1840 | C2 | semidirect |
| 120. #1840 | D79 | semidirect |
| 124. C79 | #21670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23766698 | 2 |
| #23764011 | 2 |
| #23763962 | 2 |
| #23763271 | 2 |
| #23763180 | 2 |
| #23763087 | 2 |
| C79×#1840 | 2 |
| #21670 | 79 |