Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1546 conjugacy classes of subgroups; only the 395 normal subgroups are shown.
This group has 1546 conjugacy classes of subgroups — too many to draw. Only its 395 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 |
|---|---|---|
| 2. #23763474 | C2 | semidirect |
| 3. #23763133 | C2 | semidirect |
| 11. C2×C4×D4×C79 | C4 | semidirect |
| 99. C79 | #20690 | semidirect |
| 102. C2×C4×D4 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765982 | 2 |
| #23763474 | 2 |
| #23763133 | 2 |
| C2×#518×C79 | 2 |
| #20690 | 79 |