Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
406 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 406 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 |
|---|---|---|
| 1. #23757993 | C2 | semidirect |
| 2. #23757944 | C2 | semidirect |
| 3. #23757661 | C2 | semidirect |
| 4. #23757646 | C2 | semidirect |
| 5. #23757487 | C2 | semidirect |
| 6. #23757478 | C2 | semidirect |
| 7. #23757472 | C2 | semidirect |
| 8. #23757468 | C2 | semidirect |
| 9. #23757403 | C2 | semidirect |
| 10. #23757372 | C2 | semidirect |
| 11. C4×D8×C157 | C2 | semidirect |
| 106. C8×C157 | #41 | semidirect |
| 132. C157 | #3397 | semidirect |
| 144. C4×D8 | D157 | semidirect |
| 239. C8 | #14578954 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757993 | 2 |
| #23757944 | 2 |
| #23757661 | 2 |
| #23757646 | 2 |
| #23757487 | 2 |
| #23757478 | 2 |
| #23757472 | 2 |
| #23757468 | 2 |
| #23757403 | 2 |
| #23757372 | 2 |
| C4×D8×C157 | 2 |
| #3397 | 157 |