Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
312 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 97 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. #14521102 | C2 | semidirect |
| 3. #14520778 | C2 | semidirect |
| 4. C31×#431 | C2 | semidirect |
| 16. C4×C8×C31 | C22 | semidirect |
| 18. C4⋊(C31⋊C8) | C22 | semidirect |
| 27. C2×D124 | C8 | semidirect |
| 85. #431 | D31 | semidirect |
| 106. C4×C8 | C2×D31 | semidirect |
| 107. C31 | #1478 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D124 | 2 |
| #14521102 | 2 |
| #14520778 | 2 |
| C31×#431 | 2 |
| #1478 | 31 |