Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
188 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 61 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. #14521249 | C2 | semidirect |
| 3. #14520802 | C2 | semidirect |
| 4. #14520792 | C2 | semidirect |
| 5. C8×Q8×C31 | C2 | semidirect |
| 34. Q8×C31 | D8 | semidirect |
| 47. C8×C31 | SD16 | semidirect |
| 63. C8×Q8 | D31 | semidirect |
| 81. C31 | #1668 | semidirect |
| 99. Q8 | D248 | semidirect |
| 113. C8 | #92481 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521426 | 2 |
| #14521249 | 2 |
| #14520802 | 2 |
| #14520792 | 2 |
| C8×Q8×C31 | 2 |
| #1668 | 31 |