Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
760 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 165 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. C22×#14578944 | C2 | semidirect |
| 3. C22×#14578941 | C2 | semidirect |
| 4. #23757433 | C2 | direct (N × H) |
| 5. C2×#19097694 | C2 | semidirect |
| 6. C2×#19097691 | C2 | semidirect |
| 7. C2×C22⋊#11929434 | C2 | semidirect |
| 8. C2×C22⋊Q8×C157 | C2 | semidirect |
| 18. C2×#14578944 | C22 | semidirect |
| 20. C2×#14578941 | C22 | semidirect |
| 23. #19097694 | C22 | semidirect |
| 24. #19097691 | C22 | semidirect |
| 25. C22⋊#11929434 | C22 | semidirect |
| 29. C22⋊Q8×C157 | C22 | semidirect |
| 130. C2×C157 | #452 | semidirect |
| 135. C157 | C2×#452 | semidirect |
| 140. C2×C22⋊Q8 | D157 | semidirect |
| 162. C22⋊Q8 | C2×D157 | semidirect |
| 267. C2 | #23757433 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14578954 | 2 |
| C22×#14578944 | 2 |
| C22×#14578941 | 2 |
| #23757433 | 2 |
| C2×#19097694 | 2 |
| C2×#19097691 | 2 |
| C2×C22⋊#11929434 | 2 |
| C2×C22⋊Q8×C157 | 2 |
| C2×#452 | 157 |