Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
584 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 137 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×#19097797 | C2 | semidirect |
| 3. C2×#19097767 | C2 | semidirect |
| 4. #23757741 | C2 | semidirect |
| 5. #23757472 | C2 | semidirect |
| 6. #23757467 | C2 | semidirect |
| 7. #23757296 | C2 | semidirect |
| 8. #23757277 | C2 | semidirect |
| 9. #418×C157 | C2 | semidirect |
| 15. C2×#14578943 | C22 | semidirect |
| 16. C2×#14578942 | C22 | semidirect |
| 17. C2×D1256 | C22 | semidirect |
| 18. C2×#14578939 | C22 | semidirect |
| 23. #19097736 | C22 | semidirect |
| 24. #19097733 | C22 | semidirect |
| 29. #19097700 | C22 | semidirect |
| 30. #19097691 | C22 | semidirect |
| 34. #102×C157 | C22 | semidirect |
| 37. #14578954 | D4 | semidirect |
| 79. Dic314 | C2×D4 | semidirect |
| 84. D628 | C2×D4 | semidirect |
| 125. Dic157 | AGL(1,ℤ/8) | semidirect |
| 132. C157 | #3038 | semidirect |
| 142. #418 | D157 | semidirect |
| 167. #102 | C2×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097799 | 2 |
| C2×#19097797 | 2 |
| C2×#19097767 | 2 |
| #23757741 | 2 |
| #23757472 | 2 |
| #23757467 | 2 |
| #23757296 | 2 |
| #23757277 | 2 |
| #418×C157 | 2 |
| #3038 | 157 |