Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#11758496 | C2 | semidirect |
| 2. #14521721 | C2 | semidirect |
| 3. #14521426 | C2 | semidirect |
| 4. #14521286 | C2 | semidirect |
| 5. #14521249 | C2 | semidirect |
| 6. #14521197 | C2 | semidirect |
| 7. C8×D124 | C2 | semidirect |
| 8. C4×Q16×C31 | C2 | semidirect |
| 40. Q16×C31 | D4 | semidirect |
| 89. C4×C31 | #135 | semidirect |
| 99. C4×Q16 | D31 | semidirect |
| 126. C31 | #3287 | semidirect |
| 138. Q16 | D124 | semidirect |
| 187. C4 | #11758496 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758496 | 2 |
| #14521721 | 2 |
| #14521426 | 2 |
| #14521286 | 2 |
| #14521249 | 2 |
| #14521197 | 2 |
| C8×D124 | 2 |
| C4×Q16×C31 | 2 |
| #3287 | 31 |