Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
316 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 73 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. #14521105 | C2 | semidirect |
| 3. C4×#92469 | C2 | semidirect |
| 4. #14520778 | C2 | semidirect |
| 5. D4⋊(C31⋊C8) | C2 | semidirect |
| 6. #14520776 | C2 | semidirect |
| 7. C31×D4⋊C8 | C2 | semidirect |
| 20. C31×C4⋊C8 | C22 | semidirect |
| 21. C4×C8×C31 | C22 | semidirect |
| 25. C4⋊(C31⋊C8) | C22 | semidirect |
| 26. C4×C31⋊C8 | C22 | semidirect |
| 66. D4×C31 | M16 | semidirect |
| 80. D124 | M16 | semidirect |
| 122. D4⋊C8 | D31 | semidirect |
| 142. C4⋊C8 | C2×D31 | semidirect |
| 147. C4×C8 | C2×D31 | semidirect |
| 148. C31 | #1490 | semidirect |
| 191. D4 | #92469 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D4×D31 | 2 |
| #14521105 | 2 |
| C4×#92469 | 2 |
| #14520778 | 2 |
| D4⋊(C31⋊C8) | 2 |
| #14520776 | 2 |
| C31×D4⋊C8 | 2 |
| #1490 | 31 |