Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
366 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 163 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 |
|---|---|---|
| 7. #19098965 | C4 | semidirect |
| 90. C79 | #13281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098965 | 2 |
| #23763564 | 2 |
| #23761492 | 2 |
| C2×C4×C16×C79 | 2 |
| #13281 | 79 |