Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
336 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 2. #23757616 | C2 | semidirect |
| 3. #23757610 | C2 | semidirect |
| 4. #23757577 | C2 | semidirect |
| 5. #23757532 | C2 | semidirect |
| 6. C4×Dic628 | C2 | semidirect |
| 8. #23757312 | C2 | semidirect |
| 9. #499×C157 | C2 | semidirect |
| 96. C157 | #3352 | semidirect |
| 99. #499 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757961 | 2 |
| #23757616 | 2 |
| #23757610 | 2 |
| #23757577 | 2 |
| #23757532 | 2 |
| C4×Dic628 | 2 |
| #23757352 | 2 |
| #23757312 | 2 |
| #499×C157 | 2 |
| #3352 | 157 |