Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 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 |
|---|---|---|
| 1. C2×#19097791 | C2 | semidirect |
| 2. #23757823 | C2 | semidirect |
| 3. #23757668 | C2 | semidirect |
| 4. #23757665 | C2 | semidirect |
| 5. #23757663 | C2 | semidirect |
| 6. #23757660 | C2 | semidirect |
| 7. C2×#19097682 | C2 | semidirect |
| 8. #532×C157 | C2 | semidirect |
| 40. C2×#11929434 | D4 | semidirect |
| 97. C157 | #3150 | semidirect |
| 101. #532 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097791 | 2 |
| #23757823 | 2 |
| #23757668 | 2 |
| #23757665 | 2 |
| #23757663 | 2 |
| #23757660 | 2 |
| C2×#19097682 | 2 |
| #532×C157 | 2 |
| #3150 | 157 |