Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
31656 conjugacy classes of subgroups; only the 6537 normal subgroups are shown.
This group has 31656 conjugacy classes of subgroups — too many to draw. Only its 6537 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C25 | C2×C3⋊D3 |
| commutator, cosocle | C2×C32 | C26 |
| Frattini | C2 | C25×C3⋊D3 |
| Fitting | C26×C32 | C2 |
| socle | C25×C32 | C22 |
| hypercenter | C26 | C3⋊D3 |
| hypocenter | C32 | C24×D4 |
| LCS | G ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C25 ◁ C26 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C26×C32 | C2 | semidirect |
| 2. C25×C3⋊D3 | C2 | semidirect |
| 3. C23×#638 | C2 | direct (N × H) |
| 4. C24×C3⋊Dic3 | C2 | semidirect |
| 8. C25×C32 | C22 | semidirect |
| 10. C24×C3⋊D3 | C22 | semidirect |
| 11. C22×#638 | C22 | direct (N × H) |
| 12. C23×C3⋊Dic3 | C22 | semidirect |
| 13. C26×C3 | D3 | semidirect |
| 18. C24×C32 | D4 | semidirect |
| 20. C24×C32 | C23 | semidirect |
| 22. C23×C3⋊D3 | C23 | semidirect |
| 23. C2×#638 | C23 | direct (N × H) |
| 24. C22×C3⋊Dic3 | C23 | semidirect |
| 28. C25×C3 | C2×D3 | semidirect |
| 34. C23×C32 | C2×D4 | semidirect |
| 36. C23×C32 | C24 | semidirect |
| 38. C22×C3⋊D3 | C24 | semidirect |
| 39. #638 | C24 | direct (N × H) |
| 40. C2×C3⋊Dic3 | C24 | semidirect |
| 42. C26 | C3⋊D3 | semidirect |
| 46. C24×C3 | #67 | semidirect |
| 48. C24×C3 | C22×D3 | semidirect |
| 54. C22×C32 | C22×D4 | semidirect |
| 56. C22×C32 | C25 | semidirect |
| 58. C2×C3⋊D3 | C25 | semidirect |
| 59. C3⋊Dic3 | C25 | semidirect |
| 64. C25 | C2×C3⋊D3 | semidirect |
| 68. C23×C3 | C2×#67 | semidirect |
| 70. C23×C3 | C23×D3 | semidirect |
| 76. C2×C32 | C23×D4 | semidirect |
| 82. C24 | #638 | direct (N × H) |
| 84. C24 | C22×C3⋊D3 | semidirect |
| 88. C22×C3 | C22×#67 | semidirect |
| 90. C22×C3 | C24×D3 | semidirect |
| 94. C32 | C24×D4 | semidirect |
| 98. C23 | C2×#638 | direct (N × H) |
| 100. C23 | C23×C3⋊D3 | semidirect |
| 104. C2×C3 | C23×#67 | semidirect |
| 110. C22 | C22×#638 | direct (N × H) |
| 112. C22 | C24×C3⋊D3 | semidirect |
| 114. C3 | C24×#67 | semidirect |
| 117. C2 | C23×#638 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C26×C32 | 2 |
| C25×C3⋊D3 | 2 |
| C23×#638 | 2 |
| C24×C3⋊Dic3 | 2 |
| C24×#67 | 3 |