Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
456 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 129 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. #23757818 | C2 | semidirect |
| 2. #23757677 | C2 | semidirect |
| 3. #23757648 | C2 | semidirect |
| 4. #23757618 | C2 | semidirect |
| 5. #23757509 | C2 | semidirect |
| 6. #23757507 | C2 | semidirect |
| 7. D8×Dic157 | C2 | semidirect |
| 8. #23757355 | C2 | semidirect |
| 9. #23757353 | C2 | semidirect |
| 10. C2×C8×Dic157 | C2 | semidirect |
| 11. #466×C157 | C2 | semidirect |
| 82. C2×Dic157 | D8 | semidirect |
| 89. #11929434 | #41 | semidirect |
| 101. C8×C157 | #41 | semidirect |
| 127. C157 | #3169 | semidirect |
| 135. #466 | D157 | semidirect |
| 229. C8 | #14578953 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757818 | 2 |
| #23757677 | 2 |
| #23757648 | 2 |
| #23757618 | 2 |
| #23757509 | 2 |
| #23757507 | 2 |
| D8×Dic157 | 2 |
| #23757355 | 2 |
| #23757353 | 2 |
| C2×C8×Dic157 | 2 |
| #466×C157 | 2 |
| #3169 | 157 |