Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
392 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 141 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. #14521397 | C2 | semidirect |
| 3. #14521336 | C2 | semidirect |
| 4. #14521249 | C2 | semidirect |
| 5. Q8×C31⋊C8 | C2 | semidirect |
| 6. C4×#92481 | C2 | semidirect |
| 7. Q82×C31 | C2 | semidirect |
| 46. Q8×C31 | SD16 | semidirect |
| 47. Q8×C31 | #41 | semidirect |
| 73. Q82 | D31 | semidirect |
| 100. C31 | #3362 | semidirect |
| 123. Q8 | #92481 | semidirect |
| 124. Q8 | #92499 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521721 | 2 |
| #14521397 | 2 |
| #14521336 | 2 |
| #14521249 | 2 |
| Q8×C31⋊C8 | 2 |
| C4×#92481 | 2 |
| Q82×C31 | 2 |
| #3362 | 31 |