Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
1088 conjugacy classes of subgroups; only the 285 normal subgroups are shown.
This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 285 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×#11758503 | C2 | semidirect |
| 3. #14520910 | C2 | semidirect |
| 4. #14520906 | C2 | semidirect |
| 6. C4×(C2×D31)⋊C4 | C2 | semidirect |
| 7. C2×C31×#117 | C2 | semidirect |
| 13. C22×C4×D31 | C4 | semidirect |
| 17. C2×C4⋊C4×C31 | C22 | semidirect |
| 19. C2×C42×C31 | C22 | semidirect |
| 23. C2×C4⋊Dic31 | C22 | semidirect |
| 24. C2×C4×Dic31 | C22 | semidirect |
| 25. C31⋊#95 | C22 | semidirect |
| 73. C2×C4×C31 | C22⋊C4 | semidirect |
| 102. C2×D31 | #117 | semidirect |
| 110. C2×#117 | D31 | semidirect |
| 132. C2×C4⋊C4 | C2×D31 | semidirect |
| 137. C2×C42 | C2×D31 | semidirect |
| 139. C31 | #2280 | semidirect |
| 195. C2×C4 | (C2×D31)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×D31 | 2 |
| C2×#11758503 | 2 |
| #14520910 | 2 |
| #14520906 | 2 |
| #14520904 | 2 |
| C4×(C2×D31)⋊C4 | 2 |
| C2×C31×#117 | 2 |
| #2280 | 31 |