Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
456 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 189 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 |
|---|---|---|
| 3. #23757378 | C2 | semidirect |
| 4. C4×#14578944 | C2 | semidirect |
| 11. C2×#14578944 | C4 | semidirect |
| 98. C157 | #2950 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14578944 | 2 |
| #23757750 | 2 |
| #23757378 | 2 |
| C4×#14578944 | 2 |
| #23757309 | 2 |
| #23757282 | 2 |
| #23757281 | 2 |
| #23757229 | 2 |
| #519×C157 | 2 |
| #2950 | 157 |