Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
520 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 133 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×#19097794 | C2 | semidirect |
| 2. C22×C8×D157 | C2 | semidirect |
| 3. #23757786 | C2 | semidirect |
| 4. #23757511 | C2 | semidirect |
| 5. #23757510 | C2 | semidirect |
| 6. #23757509 | C2 | semidirect |
| 7. #23757505 | C2 | semidirect |
| 8. #23757504 | C2 | semidirect |
| 9. #23757310 | C2 | semidirect |
| 10. #23757268 | C2 | semidirect |
| 11. #467×C157 | C2 | semidirect |
| 15. C2×#14578941 | C22 | semidirect |
| 16. C2×D1256 | C22 | semidirect |
| 31. #19097705 | C22 | semidirect |
| 32. #19097702 | C22 | semidirect |
| 33. #19097695 | C22 | semidirect |
| 34. #19097693 | C22 | semidirect |
| 35. #19097691 | C22 | semidirect |
| 36. C2×Q16×C157 | C22 | semidirect |
| 39. #107×C157 | C22 | semidirect |
| 40. #103×C157 | C22 | semidirect |
| 64. C8×D157 | D4 | semidirect |
| 118. C22×C157 | #135 | semidirect |
| 129. C2×D157 | #135 | semidirect |
| 145. C157 | #3050 | semidirect |
| 151. #467 | D157 | semidirect |
| 161. C2×Q16 | C2×D157 | semidirect |
| 181. #107 | C2×D157 | semidirect |
| 184. #103 | C2×D157 | semidirect |
| 274. C22 | #19097794 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097794 | 2 |
| C22×C8×D157 | 2 |
| #23757786 | 2 |
| #23757511 | 2 |
| #23757510 | 2 |
| #23757509 | 2 |
| #23757505 | 2 |
| #23757504 | 2 |
| #23757310 | 2 |
| #23757268 | 2 |
| #467×C157 | 2 |
| #3050 | 157 |