Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
392 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
|---|---|---|
| 1. Q8×Dic62 | C2 | semidirect |
| 3. #14521396 | C2 | semidirect |
| 4. #14521340 | C2 | semidirect |
| 5. #14521250 | C2 | semidirect |
| 6. C4×#92470 | C2 | semidirect |
| 7. C8×Q8×C31 | C2 | semidirect |
| 44. Q8×C31 | SD16 | semidirect |
| 58. Dic62 | #41 | semidirect |
| 78. C8×Q8 | D31 | semidirect |
| 100. C31 | #3362 | semidirect |
| 124. Q8 | #92470 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic62 | 2 |
| #14521721 | 2 |
| #14521396 | 2 |
| #14521340 | 2 |
| #14521250 | 2 |
| C4×#92470 | 2 |
| C8×Q8×C31 | 2 |
| #3362 | 31 |