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. #14521411 | C2 | semidirect |
| 4. #14521409 | C2 | semidirect |
| 5. #14521408 | C2 | semidirect |
| 6. #14521398 | C2 | semidirect |
| 7. #14521394 | C2 | semidirect |
| 8. #14521049 | C2 | semidirect |
| 9. #14521047 | C2 | semidirect |
| 10. #14521001 | C2 | semidirect |
| 11. C31×#489 | C2 | semidirect |
| 140. #489 | D31 | semidirect |
| 183. C31 | #3141 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521598 | 2 |
| C4⋊Q8×D31 | 2 |
| #14521411 | 2 |
| #14521409 | 2 |
| #14521408 | 2 |
| #14521398 | 2 |
| #14521394 | 2 |
| #14521049 | 2 |
| #14521047 | 2 |
| #14521001 | 2 |
| C31×#489 | 2 |
| #3141 | 31 |