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 |
|---|---|---|
| 1. #23758001 | C2 | semidirect |
| 2. #23757627 | C2 | semidirect |
| 4. #23757573 | C2 | semidirect |
| 5. #23757558 | C2 | semidirect |
| 6. #23757492 | C2 | semidirect |
| 8. Q8×#11929434 | C2 | semidirect |
| 9. C4×#14578944 | C2 | semidirect |
| 10. C4×#14578942 | C2 | semidirect |
| 117. C157 | #3365 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23758001 | 2 |
| #23757627 | 2 |
| #23757619 | 2 |
| #23757573 | 2 |
| #23757558 | 2 |
| #23757492 | 2 |
| #23757470 | 2 |
| Q8×#11929434 | 2 |
| C4×#14578944 | 2 |
| C4×#14578942 | 2 |
| #559×C157 | 2 |
| #3365 | 157 |