Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
492 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 87 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. #23761226 | C2 | semidirect |
| 4. #23761223 | C2 | semidirect |
| 5. C79×#2809 | C2 | semidirect |
| 146. #2809 | D79 | semidirect |
| 151. C79 | #7743 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23764634 | 2 |
| #23764487 | 2 |
| #23761226 | 2 |
| #23761223 | 2 |
| C79×#2809 | 2 |
| #7743 | 79 |