Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
218 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 49 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 |
|---|---|---|
| 4. C2×#14579095 | C4 | semidirect |
| 8. #19098326 | C4 | semidirect |
| 105. C79 | #7077 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23764828 | 2 |
| #23761324 | 2 |
| C79×#1289 | 2 |
| #7077 | 79 |