Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
290 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 1. #23765624 | C2 | semidirect |
| 3. #23763010 | C2 | semidirect |
| 4. C79×#1311 | C2 | semidirect |
| 54. #1311 | D79 | semidirect |
| 55. C79 | #12513 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765624 | 2 |
| #23763015 | 2 |
| #23763010 | 2 |
| C79×#1311 | 2 |
| #12513 | 79 |