Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
392 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 125 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. #23757826 | C2 | semidirect |
| 3. #23757640 | C2 | semidirect |
| 4. #23757636 | C2 | semidirect |
| 5. #23757634 | C2 | semidirect |
| 6. #23757631 | C2 | semidirect |
| 7. #23757270 | C2 | semidirect |
| 8. #23757269 | C2 | semidirect |
| 9. #23757267 | C2 | semidirect |
| 10. C2×#19097681 | C2 | semidirect |
| 11. #416×C157 | C2 | semidirect |
| 125. C157 | #3135 | semidirect |
| 136. #416 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757826 | 2 |
| #23757819 | 2 |
| #23757640 | 2 |
| #23757636 | 2 |
| #23757634 | 2 |
| #23757631 | 2 |
| #23757270 | 2 |
| #23757269 | 2 |
| #23757267 | 2 |
| C2×#19097681 | 2 |
| #416×C157 | 2 |
| #3135 | 157 |