Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
368 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 117 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. C2×#19097790 | C2 | semidirect |
| 2. #23757702 | C2 | direct (N × H) |
| 3. C2×Dic1256 | C2 | semidirect |
| 4. C2×#19097715 | C2 | semidirect |
| 5. C2×C16×D157 | C2 | semidirect |
| 6. C2×D16×C157 | C2 | semidirect |
| 9. #19097790 | C22 | semidirect |
| 13. Dic1256 | C22 | semidirect |
| 14. #19097715 | C22 | semidirect |
| 16. C16×D157 | C22 | semidirect |
| 18. D16×C157 | C22 | semidirect |
| 64. C2×C157 | #508 | semidirect |
| 67. C157 | C2×#508 | semidirect |
| 73. C2×D16 | D157 | semidirect |
| 84. D16 | C2×D157 | semidirect |
| 133. C2 | #23757702 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097790 | 2 |
| #23757702 | 2 |
| C2×Dic1256 | 2 |
| C2×#19097715 | 2 |
| C2×C16×D157 | 2 |
| C2×D16×C157 | 2 |
| C2×#508 | 157 |