Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
442 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 123. C79⋊C8 | #101 | semidirect |
| 149. C79 | #9799 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098966 | 2 |
| #23764244 | 2 |
| #23762158 | 2 |
| #23762073 | 2 |
| #23762072 | 2 |
| M16×C79⋊C8 | 2 |
| C79×#1966 | 2 |
| #9799 | 79 |