Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 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. #23757993 | C2 | semidirect |
| 2. #23757623 | C2 | semidirect |
| 3. #23757611 | C2 | semidirect |
| 4. #23757553 | C2 | semidirect |
| 5. #23757512 | C2 | semidirect |
| 6. #23757480 | C2 | semidirect |
| 7. #23757435 | C2 | semidirect |
| 8. C4×#14578942 | C2 | semidirect |
| 9. D4×#11929434 | C2 | semidirect |
| 10. #23757269 | C2 | semidirect |
| 125. C157 | #3302 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757993 | 2 |
| #23757623 | 2 |
| #23757611 | 2 |
| #23757553 | 2 |
| #23757512 | 2 |
| #23757480 | 2 |
| #23757435 | 2 |
| C4×#14578942 | 2 |
| D4×#11929434 | 2 |
| #23757269 | 2 |
| #547×C157 | 2 |
| #3302 | 157 |