Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
310 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 2. #23758040 | C2 | semidirect |
| 3. #23757291 | C2 | semidirect |
| 4. #23757239 | C2 | semidirect |
| 5. #23757043 | C2 | semidirect |
| 6. #23757038 | C2 | semidirect |
| 7. #416×C157 | C2 | semidirect |
| 10. #19097801 | C4 | semidirect |
| 12. #19097796 | C4 | semidirect |
| 118. C157 | #1881 | semidirect |
| 123. #416 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23758071 | 2 |
| #23758040 | 2 |
| #23757291 | 2 |
| #23757239 | 2 |
| #23757043 | 2 |
| #23757038 | 2 |
| #416×C157 | 2 |
| #1881 | 157 |