Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
474 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 173. C79 | #10099 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774606 | 2 |
| #23773781 | 2 |
| #23769521 | 2 |
| #23762125 | 2 |
| #23761913 | 2 |
| #23761294 | 2 |
| C79×#1528 | 2 |
| #10099 | 79 |