Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
200 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 55. C79⋊C16 | Q16 | semidirect |
| 104. C79 | #12460 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765673 | 2 |
| #23765305 | 2 |
| #23762795 | 2 |
| #23762791 | 2 |
| #23761473 | 2 |
| #23761454 | 2 |
| C79×#1364 | 2 |
| #12460 | 79 |