Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 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 |
|---|---|---|
| 1. C2×#19097793 | C2 | semidirect |
| 2. C22×#14578937 | C2 | semidirect |
| 3. #23757785 | C2 | semidirect |
| 4. #23757532 | C2 | semidirect |
| 5. #23757527 | C2 | semidirect |
| 6. #23757520 | C2 | semidirect |
| 7. #23757267 | C2 | semidirect |
| 8. #427×C157 | C2 | semidirect |
| 12. C2×Dic628 | C22 | semidirect |
| 13. C2×#14578943 | C22 | semidirect |
| 14. C2×D1256 | C22 | semidirect |
| 24. #19097694 | C22 | semidirect |
| 25. #19097691 | C22 | semidirect |
| 28. #107×C157 | C22 | semidirect |
| 29. #106×C157 | C22 | semidirect |
| 54. C2×C8×C157 | D4 | semidirect |
| 105. C157 | #3054 | semidirect |
| 113. #427 | D157 | semidirect |
| 132. #107 | C2×D157 | semidirect |
| 133. #106 | C2×D157 | semidirect |
| 157. C2×C8 | D628 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097793 | 2 |
| C22×#14578937 | 2 |
| #23757785 | 2 |
| #23757532 | 2 |
| #23757527 | 2 |
| #23757520 | 2 |
| #23757267 | 2 |
| #427×C157 | 2 |
| #3054 | 157 |