Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
572 conjugacy classes of subgroups; only the 381 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 381 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. #23757229 | C2 | semidirect |
| 3. C4×#14578938 | C2 | semidirect |
| 4. C2×C4×#11929434 | C2 | semidirect |
| 6. #19097778 | C4 | direct (N × H) |
| 18. #14578938 | C2×C4 | semidirect |
| 19. C2×#11929434 | C2×C4 | semidirect |
| 48. C4×C157 | #131 | semidirect |
| 53. C157 | C4×#131 | semidirect |
| 102. C4 | #19097778 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097778 | 2 |
| #23757229 | 2 |
| C4×#14578938 | 2 |
| C2×C4×#11929434 | 2 |
| C4×#41×C157 | 2 |
| C4×#131 | 157 |