Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
348 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 137 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. #23757681 | C2 | semidirect |
| 4. #23757680 | C2 | semidirect |
| 5. #23757675 | C2 | semidirect |
| 6. #23757672 | C2 | semidirect |
| 7. #23757672 | C2 | semidirect |
| 11. #499×C157 | C2 | semidirect |
| 43. #14578937 | Q8 | semidirect |
| 44. #14578937 | Q8 | semidirect |
| 99. C157 | #3166 | semidirect |
| 108. #499 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757829 | 2 |
| #125×D157 | 2 |
| #23757681 | 2 |
| #23757680 | 2 |
| #23757675 | 2 |
| #23757672 | 2 |
| #23757314 | 2 |
| #23757312 | 2 |
| C4×#14578937 | 2 |
| #499×C157 | 2 |
| #3166 | 157 |