Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
656 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 3. #23761253 | C2 | semidirect |
| 12. C2×#117×C79 | C4 | semidirect |
| 13. C22×C42×C79 | C4 | semidirect |
| 18. C4×C22⋊C4×C79 | C4 | semidirect |
| 173. C79 | #8738 | semidirect |
| 175. C2×#117 | Dic79 | semidirect |
| 176. C22×C42 | Dic79 | semidirect |
| 187. C4×C22⋊C4 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23763328 | 2 |
| #23763318 | 2 |
| #23761253 | 2 |
| C79×#2297 | 2 |
| #8738 | 79 |