Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
188 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 61 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. #23757026 | C2 | semidirect |
| 4. #23757016 | C2 | semidirect |
| 5. C8×Q8×C157 | C2 | semidirect |
| 40. Q8×C157 | D8 | semidirect |
| 48. C8×C157 | SD16 | semidirect |
| 64. C157 | #1668 | semidirect |
| 68. C8×Q8 | D157 | semidirect |
| 99. Q8 | D1256 | semidirect |
| 113. C8 | #14578941 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757650 | 2 |
| #23757473 | 2 |
| #23757026 | 2 |
| #23757016 | 2 |
| C8×Q8×C157 | 2 |
| #1668 | 157 |