Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
174 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 65 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×D248 | C2 | semidirect |
| 3. #14520874 | C2 | semidirect |
| 4. #14520850 | C2 | semidirect |
| 5. #14520849 | C2 | semidirect |
| 6. C4×C31⋊C16 | C2 | semidirect |
| 7. C4×D8×C31 | C2 | semidirect |
| 15. #11758414 | C4 | direct (N × H) |
| 25. D8×C31 | C2×C4 | semidirect |
| 34. D248 | C2×C4 | semidirect |
| 36. C31⋊C16 | C2×C4 | semidirect |
| 63. C4×C31 | D16 | semidirect |
| 69. C4×D8 | D31 | semidirect |
| 91. C31 | C4×D16 | semidirect |
| 99. D8 | C4×D31 | semidirect |
| 135. C4 | #11758414 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758414 | 2 |
| C4×D248 | 2 |
| #14520874 | 2 |
| #14520850 | 2 |
| #14520849 | 2 |
| C4×C31⋊C16 | 2 |
| C4×D8×C31 | 2 |
| C4×D16 | 31 |