Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
740 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 205 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. C2×C4×D124 | C2 | semidirect |
| 3. #14520951 | C2 | semidirect |
| 4. #14520927 | C2 | semidirect |
| 5. #14520915 | C2 | semidirect |
| 6. C31×#376 | C2 | semidirect |
| 16. #11758451 | C4 | semidirect |
| 29. C2×D124 | C2×C4 | semidirect |
| 30. C2×D124 | C2×C4 | semidirect |
| 34. C42×C31 | C2×C4 | semidirect |
| 35. C42×C31 | D4 | semidirect |
| 79. #376 | D31 | semidirect |
| 98. C31 | #2328 | semidirect |
| 116. C42 | C4×D31 | semidirect |
| 117. C42 | D124 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758451 | 2 |
| C2×C4×D124 | 2 |
| #14520951 | 2 |
| #14520927 | 2 |
| #14520915 | 2 |
| C31×#376 | 2 |
| #2328 | 31 |