Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
484 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 175 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 |
|---|---|---|
| 2. #23757755 | C2 | semidirect |
| 3. #23757386 | C2 | semidirect |
| 4. #23757384 | C2 | semidirect |
| 5. #23757380 | C2 | semidirect |
| 6. C4×#14578941 | C2 | semidirect |
| 7. #23757358 | C2 | semidirect |
| 8. #106×D157 | C2 | semidirect |
| 9. #23757273 | C2 | semidirect |
| 10. #23757230 | C2 | semidirect |
| 11. #441×C157 | C2 | semidirect |
| 13. #19097794 | C4 | semidirect |
| 41. #14578955 | C2×C4 | semidirect |
| 49. #14578941 | C2×C4 | semidirect |
| 50. D1256 | C2×C4 | semidirect |
| 54. C8×D157 | C2×C4 | semidirect |
| 65. Q16×C157 | C2×C4 | semidirect |
| 114. C157 | #2952 | semidirect |
| 121. #441 | D157 | semidirect |
| 165. Q16 | C4×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097794 | 2 |
| #23757755 | 2 |
| #23757386 | 2 |
| #23757384 | 2 |
| #23757380 | 2 |
| C4×#14578941 | 2 |
| #23757358 | 2 |
| #106×D157 | 2 |
| #23757273 | 2 |
| #23757230 | 2 |
| #441×C157 | 2 |
| #2952 | 157 |