Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
286 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 5. C2×#14579101 | C4 | semidirect |
| 9. C22⋊(C79⋊C16) | C4 | semidirect |
| 116. C79 | #7201 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765011 | 2 |
| C79×#1752 | 2 |
| #7201 | 79 |