Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
326 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 93 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. #23765158 | C2 | semidirect |
| 5. #23764186 | C2 | semidirect |
| 6. #23761510 | C2 | semidirect |
| 7. C2×#368×C79 | C2 | semidirect |
| 142. C2×#368 | D79 | semidirect |
| 149. C79 | #13470 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765158 | 2 |
| C2×#19098375 | 2 |
| C2×#19098365 | 2 |
| #23764308 | 2 |
| #23764186 | 2 |
| #23761510 | 2 |
| C2×#368×C79 | 2 |
| #13470 | 79 |