Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
266 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 53 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×D8×D157 | C2 | semidirect |
| 2. C2×D2512 | C2 | semidirect |
| 3. C2×#19097712 | C2 | semidirect |
| 4. #23757510 | C2 | semidirect |
| 5. #23757073 | C2 | semidirect |
| 6. #23757052 | C2 | semidirect |
| 7. #357×C157 | C2 | semidirect |
| 10. C2×D1256 | C22 | semidirect |
| 18. C2×#14578929 | C22 | semidirect |
| 21. C2×C16×C157 | C22 | semidirect |
| 22. #107×C157 | C22 | semidirect |
| 34. D1256 | D4 | semidirect |
| 43. D8×C157 | D4 | semidirect |
| 83. C2×D157 | D16 | semidirect |
| 95. C157 | #2184 | semidirect |
| 102. #357 | D157 | semidirect |
| 116. C2×C16 | C2×D157 | semidirect |
| 117. #107 | C2×D157 | semidirect |
| 134. D8 | D628 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×D157 | 2 |
| C2×D2512 | 2 |
| C2×#19097712 | 2 |
| #23757510 | 2 |
| #23757073 | 2 |
| #23757052 | 2 |
| #357×C157 | 2 |
| #2184 | 157 |