Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
362 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 1. #14521784 | C2 | semidirect |
| 2. #14521406 | C2 | semidirect |
| 3. #14521397 | C2 | semidirect |
| 4. #14521346 | C2 | semidirect |
| 5. #14521341 | C2 | semidirect |
| 6. #14521264 | C2 | semidirect |
| 8. Q8×C31⋊C8 | C2 | semidirect |
| 9. C4×#92480 | C2 | semidirect |
| 10. C4×#92479 | C2 | semidirect |
| 11. C31×#554 | C2 | semidirect |
| 119. #554 | D31 | semidirect |
| 163. C31 | #3361 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521784 | 2 |
| #14521406 | 2 |
| #14521397 | 2 |
| #14521346 | 2 |
| #14521341 | 2 |
| #14521264 | 2 |
| #14521244 | 2 |
| Q8×C31⋊C8 | 2 |
| C4×#92480 | 2 |
| C4×#92479 | 2 |
| C31×#554 | 2 |
| #3361 | 31 |