Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
360 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 125 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. C2×#19097704 | C2 | semidirect |
| 4. #23757035 | C2 | semidirect |
| 11. C22⋊#11929434 | C4 | semidirect |
| 22. C2×#11929434 | C2×C4 | semidirect |
| 74. C22×C157 | #107 | semidirect |
| 96. C157 | #1852 | semidirect |
| 171. C22 | #19097704 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097704 | 2 |
| C2×C22⋊#11929434 | 2 |
| #23757133 | 2 |
| #23757035 | 2 |
| C22×C4⋊C4×C157 | 2 |
| #1852 | 157 |