Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
492 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 492 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. C4×#14578955 | C2 | semidirect |
| 3. #23757386 | C2 | semidirect |
| 4. #23757384 | C2 | semidirect |
| 5. #23757380 | C2 | semidirect |
| 6. #23757376 | C2 | semidirect |
| 7. #23757371 | C2 | semidirect |
| 8. #23757308 | C2 | semidirect |
| 9. #23757268 | C2 | semidirect |
| 10. #97×D157 | 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 | #2943 | 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 |
| C4×#14578955 | 2 |
| #23757386 | 2 |
| #23757384 | 2 |
| #23757380 | 2 |
| #23757376 | 2 |
| #23757371 | 2 |
| #23757308 | 2 |
| #23757268 | 2 |
| #97×D157 | 2 |
| #441×C157 | 2 |
| #2943 | 157 |