Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
276 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 81 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. #23761502 | C2 | semidirect |
| 6. #23761497 | C2 | semidirect |
| 7. C79×#1389 | C2 | semidirect |
| 140. #1389 | D79 | semidirect |
| 143. C79 | #13500 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765182 | 2 |
| C2×#19098348 | 2 |
| #23763455 | 2 |
| #23763443 | 2 |
| #23761502 | 2 |
| #23761497 | 2 |
| C79×#1389 | 2 |
| #13500 | 79 |