Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
380 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 380 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 |
|---|---|---|
| 3. #14521459 | C2 | semidirect |
| 4. #14521458 | C2 | semidirect |
| 5. #14521455 | C2 | semidirect |
| 6. #14521453 | C2 | semidirect |
| 7. #14521446 | C2 | semidirect |
| 11. C31×#501 | C2 | semidirect |
| 79. #92469 | Q8 | semidirect |
| 102. C8×C31 | C2×Q8 | semidirect |
| 103. C31⋊C8 | C2×Q8 | semidirect |
| 126. #501 | D31 | semidirect |
| 167. C31 | #3165 | semidirect |
| 228. C8 | Q8×D31 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521605 | 2 |
| C4⋊Q8×D31 | 2 |
| #14521459 | 2 |
| #14521458 | 2 |
| #14521455 | 2 |
| #14521453 | 2 |
| #14521446 | 2 |
| #14521090 | 2 |
| #14521088 | 2 |
| #14521001 | 2 |
| C31×#501 | 2 |
| #3165 | 31 |