Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
6520 conjugacy classes of subgroups; only the 3301 normal subgroups are shown.
This group has 6520 conjugacy classes of subgroups — too many to draw. Only its 3301 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 | C2×C31 | C26 |
| Frattini | C2 | C25×D31 |
| Fitting | C23×D4×C31 | C2 |
| socle | C24×C31 | C23 |
| hypercenter | C23×D4 | D31 |
| hypocenter | C31 | C23×#41 |
| LCS | G ▷ C2×C31 ▷ C31 | |
| UCS | C1 ◁ C24 ◁ C23×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#92497 | C2 | direct (N × H) |
| 2. C23×Dic62 | C2 | semidirect |
| 3. C23×C22⋊D31 | C2 | semidirect |
| 4. C24×Dic31 | C2 | semidirect |
| 5. C23×C4×D31 | C2 | semidirect |
| 6. C23×D4×C31 | C2 | semidirect |
| 9. C22×D4×C31 | C22 | semidirect |
| 11. C22×C22⋊D31 | C22 | semidirect |
| 14. C23×Dic31 | C22 | semidirect |
| 15. C2×#92497 | C22 | direct (N × H) |
| 16. C22×C4×D31 | C22 | semidirect |
| 17. C22×Dic62 | C22 | semidirect |
| 23. C2×D4×C31 | C23 | semidirect |
| 25. C2×C22⋊D31 | C23 | semidirect |
| 28. C22×Dic31 | C23 | semidirect |
| 29. #92497 | C23 | direct (N × H) |
| 30. C2×C4×D31 | C23 | semidirect |
| 31. C2×Dic62 | C23 | semidirect |
| 33. C23×C31 | #41 | semidirect |
| 38. D4×C31 | C24 | semidirect |
| 40. C22⋊D31 | C24 | semidirect |
| 43. C2×Dic31 | C24 | semidirect |
| 44. C4×D31 | C24 | semidirect |
| 45. Dic62 | C24 | semidirect |
| 48. C22×C31 | C2×#41 | semidirect |
| 59. C23×D4 | D31 | semidirect |
| 63. C2×C31 | C22×#41 | semidirect |
| 71. C22×D4 | C2×D31 | semidirect |
| 77. C31 | C23×#41 | semidirect |
| 86. C2×D4 | C22×D31 | semidirect |
| 95. C23 | #92497 | direct (N × H) |
| 100. D4 | C23×D31 | semidirect |
| 109. C22 | C2×#92497 | direct (N × H) |
| 117. C2 | C22×#92497 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#92497 | 2 |
| C23×Dic62 | 2 |
| C23×C22⋊D31 | 2 |
| C24×Dic31 | 2 |
| C23×C4×D31 | 2 |
| C23×D4×C31 | 2 |
| C23×#41 | 31 |