Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
376 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 3. #23757583 | C2 | semidirect |
| 4. #23757582 | C2 | semidirect |
| 5. #23757569 | C2 | semidirect |
| 6. #23757568 | C2 | semidirect |
| 7. #23757555 | C2 | semidirect |
| 11. #475×C157 | C2 | semidirect |
| 47. Q8×D157 | Q8 | semidirect |
| 130. C157 | #3078 | semidirect |
| 139. #475 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757828 | 2 |
| C4×Q8×D157 | 2 |
| #23757583 | 2 |
| #23757582 | 2 |
| #23757569 | 2 |
| #23757568 | 2 |
| #23757555 | 2 |
| #23757312 | 2 |
| #23757295 | 2 |
| #23757280 | 2 |
| #475×C157 | 2 |
| #3078 | 157 |