Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
1018 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 1018 conjugacy classes of subgroups — too many to draw. Only its 165 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×#11758514 | C2 | semidirect |
| 2. #14521236 | C2 | direct (N × H) |
| 3. C2×#11758422 | C2 | semidirect |
| 4. C2×C31×H(5,𝔽2) | C2 | semidirect |
| 5. C24×D31 | C22 | semidirect |
| 7. C31×H(5,𝔽2) | C22 | semidirect |
| 12. C2×C22⋊Dic31 | C22 | semidirect |
| 14. #11758514 | C22 | semidirect |
| 16. #11758422 | C22 | semidirect |
| 18. C24×C31 | D4 | semidirect |
| 23. C23×D31 | C23 | semidirect |
| 32. C2×D4×C31 | D4 | semidirect |
| 35. C22×C4×C31 | D4 | semidirect |
| 40. C22⋊Dic31 | C23 | semidirect |
| 50. C23×C31 | C2×D4 | semidirect |
| 66. C2×C4×C31 | C2×D4 | semidirect |
| 89. C2×H(5,𝔽2) | D31 | semidirect |
| 96. C2×C31 | B(4,𝔽2) | semidirect |
| 101. H(5,𝔽2) | C2×D31 | semidirect |
| 111. C31 | C2×B(4,𝔽2) | semidirect |
| 117. C24 | C22⋊D31 | semidirect |
| 129. C2×D4 | C22⋊D31 | semidirect |
| 133. C22×C4 | C22⋊D31 | semidirect |
| 152. C23 | C2×C22⋊D31 | semidirect |
| 164. C2×C4 | C2×C22⋊D31 | semidirect |
| 187. C2 | #14521236 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758514 | 2 |
| #14521236 | 2 |
| C2×#11758422 | 2 |
| C2×C31×H(5,𝔽2) | 2 |
| C2×B(4,𝔽2) | 31 |