Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
294 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 85 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. #23765182 | C2 | semidirect |
| 5. #23763525 | C2 | semidirect |
| 6. #23761490 | C2 | semidirect |
| 7. C79×#2155 | C2 | semidirect |
| 142. #2155 | D79 | semidirect |
| 148. C79 | #13525 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765182 | 2 |
| #23765137 | 2 |
| C2×#19098369 | 2 |
| #23764296 | 2 |
| #23763525 | 2 |
| #23761490 | 2 |
| C79×#2155 | 2 |
| #13525 | 79 |