Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
342 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 117 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. #23757617 | C2 | semidirect |
| 4. #23757605 | C2 | semidirect |
| 5. #23757565 | C2 | semidirect |
| 6. #23757555 | C2 | semidirect |
| 7. #23757532 | C2 | semidirect |
| 8. C4×Dic628 | C2 | semidirect |
| 10. #23757312 | C2 | semidirect |
| 11. #498×C157 | C2 | semidirect |
| 116. C157 | #3356 | semidirect |
| 120. #498 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757997 | 2 |
| #23757984 | 2 |
| #23757617 | 2 |
| #23757605 | 2 |
| #23757565 | 2 |
| #23757555 | 2 |
| #23757532 | 2 |
| C4×Dic628 | 2 |
| #23757352 | 2 |
| #23757312 | 2 |
| #498×C157 | 2 |
| #3356 | 157 |