Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
420 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 141 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. #14521399 | C2 | semidirect |
| 3. #14521377 | C2 | semidirect |
| 4. #14521334 | C2 | semidirect |
| 5. #14521280 | C2 | semidirect |
| 6. #14521251 | C2 | semidirect |
| 7. #14521188 | C2 | semidirect |
| 8. C4×#92481 | C2 | semidirect |
| 9. D4×C31⋊C8 | C2 | semidirect |
| 10. C2×#11758423 | C2 | semidirect |
| 11. D4×Q8×C31 | C2 | semidirect |
| 83. Q8×C31 | #41 | semidirect |
| 84. D4×C31 | SD16 | semidirect |
| 124. D4×Q8 | D31 | semidirect |
| 169. C31 | #3298 | semidirect |
| 213. Q8 | #92497 | semidirect |
| 217. D4 | #92481 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521703 | 2 |
| #14521399 | 2 |
| #14521377 | 2 |
| #14521334 | 2 |
| #14521280 | 2 |
| #14521251 | 2 |
| #14521188 | 2 |
| C4×#92481 | 2 |
| D4×C31⋊C8 | 2 |
| C2×#11758423 | 2 |
| D4×Q8×C31 | 2 |
| #3298 | 31 |