Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
504 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 125 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×#11758489 | C2 | semidirect |
| 2. #14521719 | C2 | semidirect |
| 3. #14521282 | C2 | semidirect |
| 4. #14521246 | C2 | semidirect |
| 5. #14521191 | C2 | semidirect |
| 6. C4×Dic124 | C2 | semidirect |
| 7. C8×D124 | C2 | semidirect |
| 8. C31×#493 | C2 | semidirect |
| 53. Dic124 | D4 | semidirect |
| 87. C4×C31 | #135 | semidirect |
| 95. #493 | D31 | semidirect |
| 126. C31 | #3287 | semidirect |
| 187. C4 | #11758489 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758489 | 2 |
| #14521719 | 2 |
| #14521282 | 2 |
| #14521246 | 2 |
| #14521191 | 2 |
| C4×Dic124 | 2 |
| C8×D124 | 2 |
| C31×#493 | 2 |
| #3287 | 31 |