Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
348 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 149 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. #23757674 | C2 | semidirect |
| 6. #23757673 | C2 | semidirect |
| 48. #14578938 | Q8 | semidirect |
| 72. M16×C157 | Q8 | semidirect |
| 124. C157 | #3166 | semidirect |
| 176. M16 | Dic314 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757826 | 2 |
| C2×#19097762 | 2 |
| #23757681 | 2 |
| #23757680 | 2 |
| #23757674 | 2 |
| #23757673 | 2 |
| #23757316 | 2 |
| #23757315 | 2 |
| #23757313 | 2 |
| M16×Dic157 | 2 |
| #428×C157 | 2 |
| #3166 | 157 |