Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
234 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 234 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. C4×#14578938 | C2 | semidirect |
| 2. C2×#19097682 | C2 | semidirect |
| 3. #23757015 | C2 | semidirect |
| 4. #23757013 | C2 | semidirect |
| 91. C157 | #1524 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14578938 | 2 |
| C2×#19097682 | 2 |
| #23757015 | 2 |
| #23757013 | 2 |
| #529×C157 | 2 |
| #1524 | 157 |