Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
780 conjugacy classes of subgroups; only the 325 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 325 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 |
|---|---|---|
| 3. C4⋊C4×Dic31 | C2 | semidirect |
| 4. C4×(C2×D31)⋊C4 | C2 | semidirect |
| 5. #14520896 | C2 | semidirect |
| 6. #14520895 | C2 | semidirect |
| 7. #95×D31 | C2 | semidirect |
| 8. C4×C4⋊C4×C31 | C2 | semidirect |
| 20. #11758470 | C4 | semidirect |
| 21. C4×D124 | C4 | semidirect |
| 40. C2×C4×D31 | C2×C4 | semidirect |
| 41. C2×C4×D31 | C2×C4 | semidirect |
| 42. C4⋊C4×C31 | C2×C4 | semidirect |
| 44. C42×C31 | C2×C4 | semidirect |
| 45. (C2×D31)⋊C4 | C2×C4 | semidirect |
| 46. (C2×D31)⋊C4 | C2×C4 | semidirect |
| 47. C4⋊Dic31 | C2×C4 | semidirect |
| 49. C4×Dic31 | C2×C4 | semidirect |
| 74. D124 | C42 | semidirect |
| 98. C4×C4⋊C4 | D31 | semidirect |
| 127. C31 | #2275 | semidirect |
| 144. C4⋊C4 | C4×D31 | semidirect |
| 150. C42 | C4×D31 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D124 | 2 |
| C2×#11758470 | 2 |
| C4⋊C4×Dic31 | 2 |
| C4×(C2×D31)⋊C4 | 2 |
| #14520896 | 2 |
| #14520895 | 2 |
| #95×D31 | 2 |
| C4×C4⋊C4×C31 | 2 |
| #2275 | 31 |