Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
732 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 732 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×#19097818 | C2 | semidirect |
| 2. C22×#14578942 | C2 | semidirect |
| 3. #23757840 | C2 | semidirect |
| 4. #23757415 | C2 | semidirect |
| 5. #23757410 | C2 | semidirect |
| 6. #23757283 | C2 | semidirect |
| 7. #23757269 | C2 | semidirect |
| 8. #23757241 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C157 | C2 | semidirect |
| 15. C2×#14578953 | C22 | semidirect |
| 18. C2×Q8×D157 | C22 | semidirect |
| 27. #19097696 | C22 | semidirect |
| 28. #19097695 | C22 | semidirect |
| 29. #19097692 | C22 | semidirect |
| 30. #19097683 | C22 | semidirect |
| 48. C2×Dic314 | D4 | semidirect |
| 69. #41×C157 | D4 | semidirect |
| 145. C157 | #3010 | semidirect |
| 148. C2×AGL(1,ℤ/8) | D157 | semidirect |
| 191. #41 | C22⋊D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097818 | 2 |
| C22×#14578942 | 2 |
| #23757840 | 2 |
| #23757415 | 2 |
| #23757410 | 2 |
| #23757283 | 2 |
| #23757269 | 2 |
| #23757241 | 2 |
| C2×AGL(1,ℤ/8)×C157 | 2 |
| #3010 | 157 |