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. C2×#19097796 | C2 | semidirect |
| 3. C22×#14578943 | C2 | semidirect |
| 4. #23757842 | C2 | semidirect |
| 5. #23757419 | C2 | semidirect |
| 6. #23757413 | C2 | semidirect |
| 7. #23757281 | C2 | semidirect |
| 8. #23757239 | C2 | semidirect |
| 9. #416×C157 | C2 | semidirect |
| 15. C2×#14578953 | C22 | semidirect |
| 18. C2×Q8×D157 | C22 | semidirect |
| 30. #19097694 | C22 | semidirect |
| 31. #19097683 | C22 | semidirect |
| 35. #103×C157 | C22 | semidirect |
| 36. #102×C157 | C22 | semidirect |
| 49. C2×Dic314 | D4 | semidirect |
| 72. #41×C157 | D4 | semidirect |
| 145. C157 | #3010 | semidirect |
| 154. #416 | D157 | semidirect |
| 180. #103 | C2×D157 | semidirect |
| 181. #102 | C2×D157 | semidirect |
| 191. #41 | D628 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097818 | 2 |
| C2×#19097796 | 2 |
| C22×#14578943 | 2 |
| #23757842 | 2 |
| #23757419 | 2 |
| #23757413 | 2 |
| #23757281 | 2 |
| #23757239 | 2 |
| #416×C157 | 2 |
| #3010 | 157 |