Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
684 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 41. C22×Q8×C79 | Q8 | semidirect |
| 209. C79 | #10341 | semidirect |
| 229. C22×Q8 | Dic158 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23769514 | 2 |
| #23763335 | 2 |
| #23761279 | 2 |
| #23761243 | 2 |
| C79×#1446 | 2 |
| #10341 | 79 |