Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
492 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 492 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. C22×#14578943 | C2 | semidirect |
| 2. #23757844 | C2 | semidirect |
| 4. #23757519 | C2 | semidirect |
| 5. #23757502 | C2 | semidirect |
| 6. #23757311 | C2 | semidirect |
| 7. #23757283 | C2 | semidirect |
| 8. #23757279 | C2 | semidirect |
| 9. C2×#131×C157 | C2 | semidirect |
| 20. #19097750 | C22 | semidirect |
| 25. #19097705 | C22 | semidirect |
| 26. #19097703 | C22 | semidirect |
| 27. #19097696 | C22 | semidirect |
| 32. C2×M16×C157 | C22 | semidirect |
| 34. C22×C8×C157 | C22 | semidirect |
| 67. C2×C8×C157 | D4 | semidirect |
| 120. C157 | #3057 | semidirect |
| 123. C2×#131 | D157 | semidirect |
| 139. C2×M16 | C2×D157 | semidirect |
| 141. C22×C8 | C2×D157 | semidirect |
| 179. C2×C8 | C22⋊D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14578943 | 2 |
| #23757844 | 2 |
| #23757837 | 2 |
| #23757519 | 2 |
| #23757502 | 2 |
| #23757311 | 2 |
| #23757283 | 2 |
| #23757279 | 2 |
| C2×#131×C157 | 2 |
| #3057 | 157 |