Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
552 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 141 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×#19097803 | C2 | semidirect |
| 2. C2×#19097800 | C2 | semidirect |
| 4. C4⋊Q8×D157 | C2 | semidirect |
| 5. #23757668 | C2 | semidirect |
| 6. #23757667 | C2 | semidirect |
| 7. #23757665 | C2 | semidirect |
| 8. #23757651 | C2 | semidirect |
| 9. #23757644 | C2 | semidirect |
| 10. #23757225 | C2 | semidirect |
| 11. #497×C157 | C2 | semidirect |
| 63. #14578937 | D4 | semidirect |
| 124. Dic157 | #137 | semidirect |
| 130. C157 | #3152 | semidirect |
| 139. #497 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097803 | 2 |
| C2×#19097800 | 2 |
| #23757822 | 2 |
| C4⋊Q8×D157 | 2 |
| #23757668 | 2 |
| #23757667 | 2 |
| #23757665 | 2 |
| #23757651 | 2 |
| #23757644 | 2 |
| #23757225 | 2 |
| #497×C157 | 2 |
| #3152 | 157 |