Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
338 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 338 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 |
|---|---|---|
| 1. #23758003 | C2 | semidirect |
| 4. #23757625 | C2 | semidirect |
| 5. #23757557 | C2 | semidirect |
| 7. #23757484 | C2 | semidirect |
| 8. #23757400 | C2 | semidirect |
| 9. #23757379 | C2 | semidirect |
| 116. C157 | #3369 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23758003 | 2 |
| #23757993 | 2 |
| #23757631 | 2 |
| #23757625 | 2 |
| #23757557 | 2 |
| #23757494 | 2 |
| #23757484 | 2 |
| #23757400 | 2 |
| #23757379 | 2 |
| C4×#14578942 | 2 |
| #476×C157 | 2 |
| #3369 | 157 |