Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
584 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 149 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×#19097799 | C2 | semidirect |
| 2. C2×#19097768 | C2 | semidirect |
| 3. C4×#14578954 | C2 | semidirect |
| 4. #23757474 | C2 | semidirect |
| 5. #23757469 | C2 | semidirect |
| 6. #23757279 | C2 | semidirect |
| 7. #423×C157 | C2 | semidirect |
| 12. C2×#14578943 | C22 | semidirect |
| 13. C2×D1256 | C22 | semidirect |
| 17. C4×Dic314 | C22 | semidirect |
| 18. C4×D628 | C22 | semidirect |
| 23. #19097693 | C22 | semidirect |
| 26. C4⋊C8×C157 | C22 | semidirect |
| 29. #14578954 | D4 | semidirect |
| 62. Dic314 | C2×D4 | semidirect |
| 69. D628 | C2×D4 | semidirect |
| 94. C4×C157 | AGL(1,ℤ/8) | semidirect |
| 104. C157 | #3038 | semidirect |
| 111. #423 | D157 | semidirect |
| 130. C4⋊C8 | C2×D157 | semidirect |
| 201. C4 | #19097799 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097799 | 2 |
| C2×#19097768 | 2 |
| C4×#14578954 | 2 |
| #23757474 | 2 |
| #23757469 | 2 |
| #23757279 | 2 |
| #423×C157 | 2 |
| #3038 | 157 |