Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
372 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 158. C79 | #10493 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774350 | 2 |
| #23764244 | 2 |
| #23762188 | 2 |
| #23762137 | 2 |
| #23762082 | 2 |
| #23761822 | 2 |
| C79×#1299 | 2 |
| #10493 | 79 |