Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
374 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 374 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. #23757993 | C2 | semidirect |
| 2. #23757676 | C2 | semidirect |
| 3. #23757608 | C2 | semidirect |
| 4. #23757594 | C2 | semidirect |
| 5. #23757555 | C2 | semidirect |
| 6. #23757553 | C2 | semidirect |
| 7. #23757517 | C2 | semidirect |
| 8. C4×#14578942 | C2 | semidirect |
| 9. #23757351 | C2 | semidirect |
| 10. #23757313 | C2 | semidirect |
| 82. #11929434 | #41 | semidirect |
| 122. C157 | #3353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757993 | 2 |
| #23757676 | 2 |
| #23757608 | 2 |
| #23757594 | 2 |
| #23757555 | 2 |
| #23757553 | 2 |
| #23757517 | 2 |
| C4×#14578942 | 2 |
| #23757351 | 2 |
| #23757313 | 2 |
| #547×C157 | 2 |
| #3353 | 157 |