Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
868 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 868 conjugacy classes of subgroups — too many to draw. Only its 179 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 |
|---|---|---|
| 2. #23763405 | C2 | semidirect |
| 4. C2×Q8⋊(C79⋊C8) | C2 | semidirect |
| 16. #559×C79 | C4 | semidirect |
| 167. C79 | #8445 | semidirect |
| 170. #559 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23764207 | 2 |
| #23763405 | 2 |
| C2×#19098307 | 2 |
| C2×Q8⋊(C79⋊C8) | 2 |
| C2×#559×C79 | 2 |
| #8445 | 79 |