Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
236 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 120. C79 | #10646 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23762174 | 2 |
| #23762130 | 2 |
| #23761873 | 2 |
| #23761310 | 2 |
| #23761270 | 2 |
| #23761261 | 2 |
| C79×#1552 | 2 |
| #10646 | 79 |