Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
372 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 372 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. #23757904 | C2 | semidirect |
| 3. #23757640 | C2 | semidirect |
| 4. #23757631 | C2 | semidirect |
| 5. #23757626 | C2 | semidirect |
| 6. #23757622 | C2 | semidirect |
| 7. #23757283 | C2 | semidirect |
| 9. C2×#19097694 | C2 | semidirect |
| 10. #23757231 | C2 | semidirect |
| 127. C157 | #3137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757904 | 2 |
| #23757844 | 2 |
| #23757640 | 2 |
| #23757631 | 2 |
| #23757626 | 2 |
| #23757622 | 2 |
| #23757283 | 2 |
| #23757269 | 2 |
| C2×#19097694 | 2 |
| #23757231 | 2 |
| #417×C157 | 2 |
| #3137 | 157 |