Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
354 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 354 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 |
|---|---|---|
| 2. #23757984 | C2 | semidirect |
| 3. #23757616 | C2 | semidirect |
| 4. #23757588 | C2 | semidirect |
| 5. #23757565 | C2 | semidirect |
| 6. #23757560 | C2 | semidirect |
| 7. #23757520 | C2 | semidirect |
| 8. C4×#14578943 | C2 | semidirect |
| 9. #23757352 | C2 | semidirect |
| 10. #23757314 | C2 | semidirect |
| 11. #500×C157 | C2 | semidirect |
| 121. C157 | #3357 | semidirect |
| 125. #500 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757989 | 2 |
| #23757984 | 2 |
| #23757616 | 2 |
| #23757588 | 2 |
| #23757565 | 2 |
| #23757560 | 2 |
| #23757520 | 2 |
| C4×#14578943 | 2 |
| #23757352 | 2 |
| #23757314 | 2 |
| #500×C157 | 2 |
| #3357 | 157 |