Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
374 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 374 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. #23757996 | C2 | semidirect |
| 3. #23757678 | C2 | semidirect |
| 4. #23757607 | C2 | semidirect |
| 5. #23757595 | C2 | semidirect |
| 6. #23757558 | C2 | semidirect |
| 7. #23757553 | C2 | semidirect |
| 8. #23757516 | C2 | semidirect |
| 9. #23757352 | C2 | semidirect |
| 10. #23757312 | C2 | semidirect |
| 11. C4×SD16×C157 | C2 | semidirect |
| 99. C8×C157 | #41 | semidirect |
| 122. C157 | #3353 | semidirect |
| 132. C4×SD16 | D157 | semidirect |
| 222. C8 | #14578954 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757996 | 2 |
| #23757928 | 2 |
| #23757678 | 2 |
| #23757607 | 2 |
| #23757595 | 2 |
| #23757558 | 2 |
| #23757553 | 2 |
| #23757516 | 2 |
| #23757352 | 2 |
| #23757312 | 2 |
| C4×SD16×C157 | 2 |
| #3353 | 157 |