Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
724 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 724 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 |
|---|---|---|
| 2. C2×#19098719 | C2 | semidirect |
| 4. #23761765 | C2 | semidirect |
| 6. #23761287 | C2 | semidirect |
| 7. C79×#1784 | C2 | semidirect |
| 219. #1784 | D79 | semidirect |
| 223. C79 | #9989 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774207 | 2 |
| C2×#19098719 | 2 |
| C2×#19098702 | 2 |
| #23761765 | 2 |
| #23761761 | 2 |
| #23761287 | 2 |
| C79×#1784 | 2 |
| #9989 | 79 |