Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
188 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 188 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 |
|---|---|---|
| 2. #23757473 | C2 | semidirect |
| 3. Q8×#11929434 | C2 | semidirect |
| 4. #23757025 | C2 | semidirect |
| 5. #23757017 | C2 | semidirect |
| 6. #23757016 | C2 | semidirect |
| 7. #460×C157 | C2 | semidirect |
| 52. #11929434 | SD16 | semidirect |
| 55. Q8×C157 | D8 | semidirect |
| 86. C157 | #1668 | semidirect |
| 90. #460 | D157 | semidirect |
| 133. Q8 | #14578939 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757649 | 2 |
| #23757473 | 2 |
| Q8×#11929434 | 2 |
| #23757025 | 2 |
| #23757017 | 2 |
| #23757016 | 2 |
| #460×C157 | 2 |
| #1668 | 157 |