Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
658 conjugacy classes of subgroups; only the 239 normal subgroups are shown.
This group has 658 conjugacy classes of subgroups — too many to draw. Only its 239 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 |
|---|---|---|
| 110. C79 | #21676 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23766705 | 2 |
| #23764121 | 2 |
| #23763962 | 2 |
| #23763265 | 2 |
| #23763261 | 2 |
| #23763087 | 2 |
| C79×#1832 | 2 |
| #21676 | 79 |