Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
316 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 81 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. #14521106 | C2 | semidirect |
| 3. #14520778 | C2 | semidirect |
| 4. C4×M16×C31 | C2 | semidirect |
| 16. C4×C8×C31 | C22 | semidirect |
| 18. C4⋊(C31⋊C8) | C22 | semidirect |
| 60. D124 | M16 | semidirect |
| 83. C4×M16 | D31 | semidirect |
| 104. C4×C8 | C2×D31 | semidirect |
| 105. C31 | #1490 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D124 | 2 |
| #14521106 | 2 |
| #14520778 | 2 |
| C4×M16×C31 | 2 |
| #1490 | 31 |