Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
544 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 197 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×Q8×Dic31 | C2 | semidirect |
| 4. #14521152 | C2 | direct (N × H) |
| 5. C2×#11758395 | C2 | semidirect |
| 7. C2×#11758403 | C2 | semidirect |
| 8. C2×C31×#103 | C2 | semidirect |
| 15. Q8×Dic31 | C22 | semidirect |
| 16. C2×#92481 | C4 | semidirect |
| 26. C31×#103 | C22 | semidirect |
| 28. #11758403 | C22 | semidirect |
| 29. #11758395 | C22 | semidirect |
| 33. C2×Q8×C31 | C2×C4 | semidirect |
| 51. #92481 | C2×C4 | semidirect |
| 59. C2×C31⋊C8 | C2×C4 | semidirect |
| 68. Q8×C31 | C22×C4 | semidirect |
| 88. C31⋊C8 | C22×C4 | semidirect |
| 111. C2×#103 | D31 | semidirect |
| 114. C2×C31 | #440 | semidirect |
| 137. #103 | C2×D31 | semidirect |
| 140. C31 | C2×#440 | semidirect |
| 144. C2×Q8 | C4×D31 | semidirect |
| 179. Q8 | C2×C4×D31 | semidirect |
| 217. C2 | #14521152 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#92481 | 2 |
| C2×Q8×Dic31 | 2 |
| C2×#11758470 | 2 |
| #14521152 | 2 |
| C2×#11758395 | 2 |
| C2×#11758409 | 2 |
| C2×#11758403 | 2 |
| C2×C31×#103 | 2 |
| C2×#440 | 31 |