Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
172 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 57 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. Q8×#11929434 | C2 | semidirect |
| 4. #23757023 | C2 | semidirect |
| 5. #23757019 | C2 | semidirect |
| 7. #475×C157 | C2 | semidirect |
| 51. #11929434 | SD16 | semidirect |
| 55. Q8×C157 | SD16 | semidirect |
| 79. C157 | #1666 | semidirect |
| 82. #475 | D157 | semidirect |
| 126. Q8 | #14578941 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757647 | 2 |
| #23757473 | 2 |
| Q8×#11929434 | 2 |
| #23757023 | 2 |
| #23757019 | 2 |
| #23757016 | 2 |
| #475×C157 | 2 |
| #1666 | 157 |