Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
434 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 3. #23761343 | C2 | semidirect |
| 22. #14579120 | C8 | semidirect |
| 150. C79 | #11449 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23766020 | 2 |
| #23761714 | 2 |
| #23761343 | 2 |
| C79×#1458 | 2 |
| #11449 | 79 |