Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
546 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 546 conjugacy classes of subgroups — too many to draw. Only its 139 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. #23761724 | C2 | semidirect |
| 4. #23761228 | C2 | semidirect |
| 5. C79×#2982 | C2 | semidirect |
| 24. #14579150 | C8 | semidirect |
| 150. #2982 | D79 | semidirect |
| 155. C79 | #9102 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23766107 | 2 |
| #23761792 | 2 |
| #23761724 | 2 |
| #23761228 | 2 |
| C79×#2982 | 2 |
| #9102 | 79 |