Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
564 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 137 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×#19097794 | C2 | semidirect |
| 2. C2×#19097792 | C2 | semidirect |
| 3. #23757824 | C2 | semidirect |
| 4. #23757822 | C2 | semidirect |
| 5. #23757666 | C2 | semidirect |
| 6. #23757665 | C2 | semidirect |
| 7. #23757663 | C2 | semidirect |
| 8. #23757662 | C2 | semidirect |
| 9. #23757659 | C2 | semidirect |
| 10. #97×D157 | C2 | semidirect |
| 11. #497×C157 | C2 | semidirect |
| 65. C8×D157 | D4 | semidirect |
| 133. C157 | #3150 | semidirect |
| 141. #497 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097794 | 2 |
| C2×#19097792 | 2 |
| #23757824 | 2 |
| #23757822 | 2 |
| #23757666 | 2 |
| #23757665 | 2 |
| #23757663 | 2 |
| #23757662 | 2 |
| #23757659 | 2 |
| #97×D157 | 2 |
| #497×C157 | 2 |
| #3150 | 157 |