Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
382 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 117 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. #23758002 | C2 | semidirect |
| 3. #23757636 | C2 | semidirect |
| 4. #23757619 | C2 | semidirect |
| 5. #23757571 | C2 | semidirect |
| 6. #23757554 | C2 | semidirect |
| 7. #23757471 | C2 | semidirect |
| 8. #23757400 | C2 | semidirect |
| 9. #23757374 | C2 | semidirect |
| 10. C4×#14578941 | C2 | semidirect |
| 11. #460×C157 | C2 | semidirect |
| 91. Q8×C157 | #41 | semidirect |
| 124. C157 | #3368 | semidirect |
| 133. #460 | D157 | semidirect |
| 204. Q8 | #14578953 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23758002 | 2 |
| #23757943 | 2 |
| #23757636 | 2 |
| #23757619 | 2 |
| #23757571 | 2 |
| #23757554 | 2 |
| #23757471 | 2 |
| #23757400 | 2 |
| #23757374 | 2 |
| C4×#14578941 | 2 |
| #460×C157 | 2 |
| #3368 | 157 |