Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
816 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 229 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×#92469 | C2 | semidirect |
| 3. C2×C4⋊C4×D31 | C2 | semidirect |
| 4. #14521049 | C2 | direct (N × H) |
| 5. C2×#11758423 | C2 | semidirect |
| 6. C2×#11758409 | C2 | semidirect |
| 7. C2×#11758397 | C2 | semidirect |
| 8. C2×C31×#103 | C2 | semidirect |
| 12. C2×#92499 | C4 | semidirect |
| 25. C2×#92469 | C22 | semidirect |
| 27. C4⋊C4×D31 | C22 | semidirect |
| 28. C31×#103 | C22 | semidirect |
| 29. #11758423 | C22 | semidirect |
| 30. #11758409 | C22 | semidirect |
| 31. #11758397 | C22 | semidirect |
| 36. C2×Q8×C31 | C2×C4 | semidirect |
| 45. #92499 | C2×C4 | semidirect |
| 50. C2×D124 | C2×C4 | semidirect |
| 81. Q8×C31 | C22×C4 | semidirect |
| 97. D124 | C22×C4 | semidirect |
| 130. C2×#103 | D31 | semidirect |
| 133. C2×C31 | #417 | semidirect |
| 159. #103 | C2×D31 | semidirect |
| 162. C31 | C2×#417 | semidirect |
| 170. C2×Q8 | C4×D31 | semidirect |
| 212. Q8 | C2×C4×D31 | semidirect |
| 257. C2 | #14521049 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#92499 | 2 |
| C22×#92469 | 2 |
| C2×C4⋊C4×D31 | 2 |
| #14521049 | 2 |
| C2×#11758423 | 2 |
| C2×#11758409 | 2 |
| C2×#11758397 | 2 |
| C2×C31×#103 | 2 |
| C2×#417 | 31 |