Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
420 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 420 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. Q8×D124 | C2 | semidirect |
| 3. #14521401 | C2 | semidirect |
| 4. #14521381 | C2 | semidirect |
| 5. #14521279 | C2 | semidirect |
| 6. #14521255 | C2 | semidirect |
| 7. #14521189 | C2 | semidirect |
| 8. C4×#92481 | C2 | semidirect |
| 9. #14521114 | C2 | semidirect |
| 10. #103×D31 | C2 | semidirect |
| 11. C31×#475 | C2 | semidirect |
| 81. Q8×C31 | #41 | semidirect |
| 94. D124 | SD16 | semidirect |
| 128. #475 | D31 | semidirect |
| 169. C31 | #3298 | semidirect |
| 213. Q8 | #92499 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D124 | 2 |
| #14521702 | 2 |
| #14521401 | 2 |
| #14521381 | 2 |
| #14521279 | 2 |
| #14521255 | 2 |
| #14521189 | 2 |
| C4×#92481 | 2 |
| #14521114 | 2 |
| #103×D31 | 2 |
| C31×#475 | 2 |
| #3298 | 31 |