Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
348 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 348 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. #23758001 | C2 | semidirect |
| 3. #23757628 | C2 | semidirect |
| 5. #23757574 | C2 | semidirect |
| 6. #23757559 | C2 | semidirect |
| 7. #23757496 | C2 | semidirect |
| 9. C4×Dic628 | C2 | semidirect |
| 10. C4×#14578943 | C2 | semidirect |
| 11. C8×Q8×C157 | C2 | semidirect |
| 117. C157 | #3365 | semidirect |
| 127. C8×Q8 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23758008 | 2 |
| #23758001 | 2 |
| #23757628 | 2 |
| #23757620 | 2 |
| #23757574 | 2 |
| #23757559 | 2 |
| #23757496 | 2 |
| #23757474 | 2 |
| C4×Dic628 | 2 |
| C4×#14578943 | 2 |
| C8×Q8×C157 | 2 |
| #3365 | 157 |