Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
488 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 488 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. C2×#19097763 | C2 | semidirect |
| 3. #23757638 | C2 | direct (N × H) |
| 4. C2×#19097693 | C2 | semidirect |
| 5. C2×#97×C157 | C2 | semidirect |
| 11. #19097763 | C22 | semidirect |
| 14. #19097693 | C22 | semidirect |
| 17. #97×C157 | C22 | semidirect |
| 59. C2×C157 | #490 | semidirect |
| 63. C157 | C2×#490 | semidirect |
| 69. C2×#97 | D157 | semidirect |
| 81. #97 | C2×D157 | semidirect |
| 124. C2 | #23757638 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097768 | 2 |
| C2×#19097763 | 2 |
| #23757638 | 2 |
| C2×#19097693 | 2 |
| C2×#97×C157 | 2 |
| C2×#490 | 157 |