Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
392 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 141 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. #23757621 | C2 | semidirect |
| 3. #23757560 | C2 | semidirect |
| 4. #23757473 | C2 | semidirect |
| 5. Q8×#11929434 | C2 | semidirect |
| 6. C4×#14578941 | C2 | semidirect |
| 7. Q82×C157 | C2 | semidirect |
| 54. Q8×C157 | SD16 | semidirect |
| 55. Q8×C157 | #41 | semidirect |
| 76. C157 | #3362 | semidirect |
| 78. Q82 | D157 | semidirect |
| 123. Q8 | #14578941 | semidirect |
| 124. Q8 | #14578955 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757945 | 2 |
| #23757621 | 2 |
| #23757560 | 2 |
| #23757473 | 2 |
| Q8×#11929434 | 2 |
| C4×#14578941 | 2 |
| Q82×C157 | 2 |
| #3362 | 157 |