Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
342 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 3. #23757669 | C2 | semidirect |
| 4. #23757616 | C2 | semidirect |
| 5. #23757602 | C2 | semidirect |
| 6. #23757559 | C2 | semidirect |
| 7. #23757530 | C2 | semidirect |
| 8. C4×#14578944 | C2 | semidirect |
| 10. #23757314 | C2 | semidirect |
| 11. #477×C157 | C2 | semidirect |
| 116. C157 | #3356 | semidirect |
| 123. #477 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757996 | 2 |
| #23757984 | 2 |
| #23757669 | 2 |
| #23757616 | 2 |
| #23757602 | 2 |
| #23757559 | 2 |
| #23757530 | 2 |
| C4×#14578944 | 2 |
| #23757350 | 2 |
| #23757314 | 2 |
| #477×C157 | 2 |
| #3356 | 157 |