Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
448 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 2. C22×Dic628 | C2 | semidirect |
| 3. #23757548 | C2 | direct (N × H) |
| 4. C2×#19097707 | C2 | semidirect |
| 5. C2×#19097689 | C2 | semidirect |
| 13. C2×Dic628 | C22 | semidirect |
| 17. #19097707 | C22 | semidirect |
| 18. #19097689 | C22 | semidirect |
| 101. C2×C157 | #473 | semidirect |
| 103. C157 | C2×#473 | semidirect |
| 205. C2 | #23757548 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097801 | 2 |
| C22×Dic628 | 2 |
| #23757548 | 2 |
| C2×#19097707 | 2 |
| C2×#19097689 | 2 |
| C2×#131×C157 | 2 |
| C2×#473 | 157 |