Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
424 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 121 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. C4×Q8×D31 | C2 | semidirect |
| 3. #14521364 | C2 | semidirect |
| 4. #14521341 | C2 | semidirect |
| 5. #14521250 | C2 | semidirect |
| 6. #14521249 | C2 | semidirect |
| 7. #14521189 | C2 | semidirect |
| 8. #14521152 | C2 | semidirect |
| 9. #14521148 | C2 | semidirect |
| 10. #14521105 | C2 | semidirect |
| 11. C31×#477 | C2 | semidirect |
| 87. Q8×C31 | #41 | semidirect |
| 113. Dic62 | #41 | semidirect |
| 140. #477 | D31 | semidirect |
| 183. C31 | #3112 | semidirect |
| 231. Q8 | #92499 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521600 | 2 |
| C4×Q8×D31 | 2 |
| #14521364 | 2 |
| #14521341 | 2 |
| #14521250 | 2 |
| #14521249 | 2 |
| #14521189 | 2 |
| #14521152 | 2 |
| #14521148 | 2 |
| #14521105 | 2 |
| C31×#477 | 2 |
| #3112 | 31 |