Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
486 conjugacy classes of subgroups; only the 235 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 235 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 |
|---|---|---|
| 9. C8×C79⋊C8 | C4 | semidirect |
| 55. C8×C79 | #106 | semidirect |
| 56. C79⋊C8 | #106 | semidirect |
| 76. C79 | #8813 | semidirect |
| 128. C8 | #14579092 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23763557 | 2 |
| #23763556 | 2 |
| C2×C8×C79⋊C8 | 2 |
| C79×#1844 | 2 |
| #8813 | 79 |