Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
206 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 54. C79⋊C16 | Q16 | semidirect |
| 105. C79 | #12053 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765305 | 2 |
| Q8×C79⋊C16 | 2 |
| C8×#11929614 | 2 |
| #23761469 | 2 |
| #23761380 | 2 |
| #23761316 | 2 |
| C79×Q8⋊C16 | 2 |
| #12053 | 79 |