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 |
|---|---|---|
| 2. C2×C4×Dic314 | C2 | semidirect |
| 3. #23757609 | C2 | semidirect |
| 5. #23757581 | C2 | semidirect |
| 6. #23757496 | C2 | semidirect |
| 7. #23757431 | C2 | semidirect |
| 9. #23757381 | C2 | semidirect |
| 10. #23757375 | C2 | semidirect |
| 11. #432×C157 | C2 | semidirect |
| 131. C157 | #3117 | semidirect |
| 143. #432 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757807 | 2 |
| C2×C4×Dic314 | 2 |
| #23757609 | 2 |
| #23757592 | 2 |
| #23757581 | 2 |
| #23757496 | 2 |
| #23757431 | 2 |
| #23757414 | 2 |
| #23757381 | 2 |
| #23757375 | 2 |
| #432×C157 | 2 |
| #3117 | 157 |