Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
528 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 181 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. #14521397 | C2 | direct (N × H) |
| 3. C2×#11758397 | C2 | semidirect |
| 4. C2×C4×C31⋊C8 | C2 | semidirect |
| 5. C2×C31×C4⋊Q8 | C2 | semidirect |
| 11. C31×C4⋊Q8 | C22 | semidirect |
| 18. #11758397 | C22 | semidirect |
| 19. C4×C31⋊C8 | C22 | semidirect |
| 75. C2×C4⋊Q8 | D31 | semidirect |
| 80. C2×C31 | #486 | semidirect |
| 91. C4⋊Q8 | C2×D31 | semidirect |
| 99. C31 | C2×#486 | semidirect |
| 155. C2 | #14521397 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758451 | 2 |
| #14521397 | 2 |
| C2×#11758397 | 2 |
| C2×C4×C31⋊C8 | 2 |
| C2×C31×C4⋊Q8 | 2 |
| C2×#486 | 31 |