Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
812 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 812 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 |
|---|---|---|
| 1. C22×#14578955 | C2 | semidirect |
| 2. C22×#14578941 | C2 | semidirect |
| 3. C22×D1256 | C2 | semidirect |
| 4. C2×#19097746 | C2 | semidirect |
| 5. #23757421 | C2 | direct (N × H) |
| 6. C2×#19097691 | C2 | semidirect |
| 7. C2×#19097683 | C2 | semidirect |
| 8. C2×#103×C157 | C2 | semidirect |
| 12. C2×#14578955 | C22 | semidirect |
| 20. C2×#14578941 | C22 | semidirect |
| 22. C2×D1256 | C22 | semidirect |
| 25. #19097746 | C22 | semidirect |
| 27. #19097691 | C22 | semidirect |
| 28. #19097683 | C22 | semidirect |
| 32. #103×C157 | C22 | semidirect |
| 48. C2×D628 | D4 | semidirect |
| 65. C2×Q8×C157 | D4 | semidirect |
| 93. D628 | C2×D4 | semidirect |
| 104. Q8×C157 | C2×D4 | semidirect |
| 136. C2×C157 | #449 | semidirect |
| 143. C157 | C2×#449 | semidirect |
| 150. C2×#103 | D157 | semidirect |
| 174. #103 | C2×D157 | semidirect |
| 185. C2×Q8 | D628 | semidirect |
| 233. Q8 | C2×D628 | semidirect |
| 283. C2 | #23757421 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14578955 | 2 |
| C22×#14578941 | 2 |
| C22×D1256 | 2 |
| C2×#19097746 | 2 |
| #23757421 | 2 |
| C2×#19097691 | 2 |
| C2×#19097683 | 2 |
| C2×#103×C157 | 2 |
| C2×#449 | 157 |