Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
256 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 57 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×#11758416 | C2 | semidirect |
| 3. #14520849 | C2 | semidirect |
| 4. C22⋊(C31⋊C16) | C2 | semidirect |
| 5. C31×#467 | C2 | semidirect |
| 7. C2×Q16×C31 | C22 | semidirect |
| 13. C31×#107 | C22 | semidirect |
| 16. C2×C31⋊C16 | C22 | semidirect |
| 56. C22×C31 | SD32 | semidirect |
| 69. #467 | D31 | semidirect |
| 78. C2×Q16 | C2×D31 | semidirect |
| 86. #107 | C2×D31 | semidirect |
| 88. C31 | #2187 | semidirect |
| 131. C22 | #11758416 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D248 | 2 |
| C2×#11758416 | 2 |
| #14520849 | 2 |
| C22⋊(C31⋊C16) | 2 |
| C31×#467 | 2 |
| #2187 | 31 |