Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
166 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 65 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. #23757025 | C2 | semidirect |
| 4. Q8⋊#11929434 | C2 | semidirect |
| 6. #23756995 | C2 | semidirect |
| 7. C8×Q8×C157 | C2 | semidirect |
| 52. Q8×C157 | M16 | semidirect |
| 77. C157 | #1588 | semidirect |
| 79. C8×Q8 | D157 | semidirect |
| 121. Q8 | #14578937 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14578941 | 2 |
| #23757352 | 2 |
| #23757025 | 2 |
| Q8⋊#11929434 | 2 |
| #23757000 | 2 |
| #23756995 | 2 |
| C8×Q8×C157 | 2 |
| #1588 | 157 |