Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
396 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 123 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. #23757621 | C2 | semidirect |
| 3. #23757597 | C2 | semidirect |
| 4. #23757555 | C2 | semidirect |
| 5. #23757504 | C2 | semidirect |
| 6. #23757473 | C2 | semidirect |
| 7. #23757433 | C2 | semidirect |
| 8. C4×#14578944 | C2 | semidirect |
| 9. D4×#11929434 | C2 | semidirect |
| 10. #23757267 | C2 | semidirect |
| 11. #556×C157 | C2 | semidirect |
| 127. C157 | #3304 | semidirect |
| 129. #556 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757944 | 2 |
| #23757621 | 2 |
| #23757597 | 2 |
| #23757555 | 2 |
| #23757504 | 2 |
| #23757473 | 2 |
| #23757433 | 2 |
| C4×#14578944 | 2 |
| D4×#11929434 | 2 |
| #23757267 | 2 |
| #556×C157 | 2 |
| #3304 | 157 |