Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
560 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 119 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 |
|---|---|---|
| 32. C22⋊(C79⋊C8) | Q8 | semidirect |
| 46. #95×C79 | Q8 | semidirect |
| 194. C79 | #10568 | semidirect |
| 235. #95 | Dic158 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23769514 | 2 |
| #23763593 | 2 |
| #23761279 | 2 |
| #23761243 | 2 |
| C79×#1442 | 2 |
| #10568 | 79 |