Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
420 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 139 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. D4×Dic62 | C2 | semidirect |
| 3. #14521400 | C2 | semidirect |
| 4. #14521380 | C2 | semidirect |
| 5. #14521335 | C2 | semidirect |
| 6. #14521278 | C2 | semidirect |
| 7. #14521255 | C2 | semidirect |
| 8. #14521190 | C2 | semidirect |
| 9. C4×#92470 | C2 | semidirect |
| 10. C2×#11758404 | C2 | semidirect |
| 11. C8×D4×C31 | C2 | semidirect |
| 79. D4×C31 | SD16 | semidirect |
| 102. Dic62 | #41 | semidirect |
| 133. C8×D4 | D31 | semidirect |
| 169. C31 | #3298 | semidirect |
| 217. D4 | #92470 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic62 | 2 |
| #14521703 | 2 |
| #14521400 | 2 |
| #14521380 | 2 |
| #14521335 | 2 |
| #14521278 | 2 |
| #14521255 | 2 |
| #14521190 | 2 |
| C4×#92470 | 2 |
| C2×#11758404 | 2 |
| C8×D4×C31 | 2 |
| #3298 | 31 |