Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
430 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 119 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. #23757821 | C2 | semidirect |
| 2. C4×#14578955 | C2 | semidirect |
| 3. #23757595 | C2 | semidirect |
| 4. #23757558 | C2 | semidirect |
| 5. #23757554 | C2 | semidirect |
| 6. #23757465 | C2 | semidirect |
| 7. #23757417 | C2 | semidirect |
| 8. #23757382 | C2 | semidirect |
| 9. #23757374 | C2 | semidirect |
| 10. #23757329 | C2 | semidirect |
| 11. #460×C157 | C2 | semidirect |
| 88. D628 | #41 | semidirect |
| 106. Q8×C157 | #41 | semidirect |
| 144. C157 | #3115 | semidirect |
| 151. #460 | D157 | semidirect |
| 233. Q8 | #14578953 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757821 | 2 |
| C4×#14578955 | 2 |
| #23757595 | 2 |
| #23757558 | 2 |
| #23757554 | 2 |
| #23757465 | 2 |
| #23757417 | 2 |
| #23757382 | 2 |
| #23757374 | 2 |
| #23757329 | 2 |
| #460×C157 | 2 |
| #3115 | 157 |