Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
384 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 180. C79 | #8775 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23766366 | 2 |
| C4×#14579079 | 2 |
| #23761743 | 2 |
| #23761293 | 2 |
| #23761266 | 2 |
| #23761265 | 2 |
| C79×#1300 | 2 |
| #8775 | 79 |