Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
380 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 125 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. #23757640 | C2 | semidirect |
| 4. #23757625 | C2 | semidirect |
| 5. #23757624 | C2 | semidirect |
| 6. #23757623 | C2 | semidirect |
| 9. #487×C157 | C2 | semidirect |
| 106. C157 | #3139 | semidirect |
| 114. #487 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757828 | 2 |
| C4⋊Q8×D157 | 2 |
| #23757640 | 2 |
| #23757625 | 2 |
| #23757624 | 2 |
| #23757623 | 2 |
| #23757280 | 2 |
| C4×#14578937 | 2 |
| #487×C157 | 2 |
| #3139 | 157 |