Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
4544 conjugacy classes of subgroups; only the 725 normal subgroups are shown.
This group has 4544 conjugacy classes of subgroups — too many to draw. Only its 725 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D31 |
| commutator, cosocle | C22×C31 | C25 |
| Frattini | C22 | C24×D31 |
| Fitting | C23×D4×C31 | C2 |
| socle | C24×C31 | C23 |
| hypercenter | C23×D4 | D31 |
| hypocenter | C31 | C22×#120 |
| LCS | G ▷ C22×C31 ▷ C31 | |
| UCS | C1 ◁ C24 ◁ C23×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C25×D31 | C2 | semidirect |
| 2. C23×C22⋊D31 | C2 | semidirect |
| 3. C2×#11758514 | C2 | direct (N × H) |
| 4. C22×C22⋊Dic31 | C2 | semidirect |
| 5. C22×(C2×D31)⋊C4 | C2 | semidirect |
| 6. C23×D4×C31 | C2 | semidirect |
| 8. C25×C31 | C22 | semidirect |
| 12. C24×D31 | C22 | semidirect |
| 14. C22×D4×C31 | C22 | semidirect |
| 15. C23×C4×C31 | C22 | semidirect |
| 17. C22×C22⋊D31 | C22 | semidirect |
| 18. C23×Dic31 | C22 | semidirect |
| 19. C2×C22⋊Dic31 | C22 | semidirect |
| 20. #11758514 | C22 | direct (N × H) |
| 21. C2×(C2×D31)⋊C4 | C22 | semidirect |
| 25. C24×C31 | D4 | semidirect |
| 28. C24×C31 | C23 | semidirect |
| 34. C23×D31 | D4 | semidirect |
| 36. C23×D31 | C23 | semidirect |
| 38. C2×D4×C31 | C23 | semidirect |
| 40. C22×C4×C31 | C23 | semidirect |
| 42. C2×C22⋊D31 | C23 | semidirect |
| 44. C22×Dic31 | C23 | semidirect |
| 45. C22⋊Dic31 | C23 | semidirect |
| 46. (C2×D31)⋊C4 | C23 | semidirect |
| 54. C23×C31 | C2×D4 | semidirect |
| 57. C23×C31 | C24 | semidirect |
| 64. C22×D31 | C2×D4 | semidirect |
| 68. C2×C4×C31 | C24 | semidirect |
| 71. C2×Dic31 | C24 | semidirect |
| 78. C22×C31 | #120 | semidirect |
| 81. C22×C31 | C22×D4 | semidirect |
| 87. C2×D31 | C22×D4 | semidirect |
| 92. C23×D4 | D31 | semidirect |
| 98. C2×C31 | C2×#120 | semidirect |
| 107. C25 | C2×D31 | semidirect |
| 111. C22×D4 | C2×D31 | semidirect |
| 113. C23×C4 | C2×D31 | semidirect |
| 117. C31 | C22×#120 | semidirect |
| 129. C24 | C22⋊D31 | semidirect |
| 132. C24 | C22×D31 | semidirect |
| 136. C2×D4 | C22×D31 | semidirect |
| 140. C22×C4 | C22×D31 | semidirect |
| 158. C23 | C2×C22⋊D31 | semidirect |
| 161. C23 | C23×D31 | semidirect |
| 167. C2×C4 | C23×D31 | semidirect |
| 178. C22 | #11758514 | direct (N × H) |
| 181. C22 | C22×C22⋊D31 | semidirect |
| 188. C2 | C2×#11758514 | 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 |
| C23×C22⋊D31 | 2 |
| C2×#11758514 | 2 |
| C22×C22⋊Dic31 | 2 |
| C22×(C2×D31)⋊C4 | 2 |
| C23×D4×C31 | 2 |
| C22×#120 | 31 |