Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
3464 conjugacy classes of subgroups; only the 429 normal subgroups are shown.
This group has 3464 conjugacy classes of subgroups — too many to draw. Only its 429 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. C22×C22⋊Dic31 | C2 | semidirect |
| 3. C22×(C2×D31)⋊C4 | C2 | semidirect |
| 4. #14520904 | C2 | direct (N × H) |
| 5. C22×C22⋊C4×C31 | C2 | semidirect |
| 10. C24×D31 | C4 | semidirect |
| 13. C23×C4×C31 | C22 | semidirect |
| 14. C23×Dic31 | C22 | semidirect |
| 16. C2×C22⋊C4×C31 | C22 | semidirect |
| 18. C2×C22⋊Dic31 | C22 | semidirect |
| 20. C2×(C2×D31)⋊C4 | C22 | semidirect |
| 38. C23×D31 | C2×C4 | semidirect |
| 43. C22×C4×C31 | C23 | semidirect |
| 46. C22×Dic31 | C23 | semidirect |
| 54. C23×C31 | C22⋊C4 | semidirect |
| 75. C22×D31 | C22⋊C4 | semidirect |
| 91. C22×C31 | C2×C22⋊C4 | semidirect |
| 104. C2×D31 | C2×C22⋊C4 | semidirect |
| 110. C22×C22⋊C4 | D31 | semidirect |
| 113. C2×C31 | #379 | semidirect |
| 127. C23×C4 | C2×D31 | semidirect |
| 133. C2×C22⋊C4 | C2×D31 | semidirect |
| 134. C31 | C2×#379 | semidirect |
| 160. C22×C4 | C22×D31 | semidirect |
| 183. C23 | (C2×D31)⋊C4 | semidirect |
| 212. C22 | C2×(C2×D31)⋊C4 | semidirect |
| 222. C2 | #14520904 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×D31 | 2 |
| C22×C22⋊Dic31 | 2 |
| C22×(C2×D31)⋊C4 | 2 |
| #14520904 | 2 |
| C22×C22⋊C4×C31 | 2 |
| C2×#379 | 31 |