Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
360 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 1. #23771673 | C2 | semidirect |
| 4. #23761428 | C2 | semidirect |
| 5. #23761427 | C2 | semidirect |
| 6. #23761343 | C2 | semidirect |
| 180. C79 | #12185 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23771673 | 2 |
| #23764626 | 2 |
| #23762437 | 2 |
| #23761428 | 2 |
| #23761427 | 2 |
| #23761343 | 2 |
| C79×#1616 | 2 |
| #12185 | 79 |