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. #23757671 | C2 | semidirect |
| 4. #23757612 | C2 | semidirect |
| 5. #23757602 | C2 | semidirect |
| 6. #23757568 | C2 | semidirect |
| 7. #23757558 | C2 | semidirect |
| 8. #23757528 | C2 | semidirect |
| 10. #23757314 | C2 | semidirect |
| 11. C4×Q16×C157 | C2 | semidirect |
| 116. C157 | #3356 | semidirect |
| 126. C4×Q16 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757996 | 2 |
| #23757983 | 2 |
| #23757671 | 2 |
| #23757612 | 2 |
| #23757602 | 2 |
| #23757568 | 2 |
| #23757558 | 2 |
| #23757528 | 2 |
| #23757352 | 2 |
| #23757314 | 2 |
| C4×Q16×C157 | 2 |
| #3356 | 157 |