Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
3960 conjugacy classes of subgroups; only the 2616 normal subgroups are shown.
This group has 3960 conjugacy classes of subgroups — too many to draw. Only its 2616 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C32 | C23 |
| commutator, Frattini, cosocle | C22 | C25×C32 |
| prime radical | C25×C32 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C32 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C32×#126 | C2 | direct (N × H) |
| 2. C22×C32×C4⋊C4 | C2 | semidirect |
| 4. C22×C32×C42 | C2 | semidirect |
| 5. C22×C3×#126 | C3 | direct (N × H) |
| 9. C32×#126 | C22 | direct (N × H) |
| 10. C2×C32×C4⋊C4 | C22 | semidirect |
| 12. C2×C32×C42 | C22 | semidirect |
| 13. C2×C3×#126 | C2×C3 | direct (N × H) |
| 14. C22×C3×C4⋊C4 | C2×C3 | semidirect |
| 16. C22×C3×C42 | C2×C3 | semidirect |
| 24. C32×C4⋊C4 | C23 | semidirect |
| 26. C32×C42 | C23 | semidirect |
| 27. C22×#126 | C32 | direct (N × H) |
| 31. C3×#126 | C22×C3 | direct (N × H) |
| 32. C2×C3×C4⋊C4 | C22×C3 | semidirect |
| 34. C2×C3×C42 | C22×C3 | semidirect |
| 44. C2×#126 | C2×C32 | direct (N × H) |
| 45. C22×C4⋊C4 | C2×C32 | semidirect |
| 47. C22×C42 | C2×C32 | semidirect |
| 55. C3×C4⋊C4 | C23×C3 | semidirect |
| 57. C3×C42 | C23×C3 | semidirect |
| 60. C22×C32 | #126 | direct (N × H) |
| 68. #126 | C22×C32 | direct (N × H) |
| 69. C2×C4⋊C4 | C22×C32 | semidirect |
| 71. C2×C42 | C22×C32 | semidirect |
| 82. C2×C32 | C2×#126 | direct (N × H) |
| 91. C4⋊C4 | C23×C32 | semidirect |
| 93. C42 | C23×C32 | semidirect |
| 96. C22×C3 | C3×#126 | direct (N × H) |
| 101. C32 | C22×#126 | direct (N × H) |
| 112. C2×C3 | C2×C3×#126 | direct (N × H) |
| 116. C22 | C32×#126 | direct (N × H) |
| 121. C3 | C22×C3×#126 | direct (N × H) |
| 123. C2 | C2×C32×#126 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×#126 | 2 |
| C22×C32×C4⋊C4 | 2 |
| C22×C32×C22⋊C4 | 2 |
| C22×C32×C42 | 2 |
| C22×C3×#126 | 3 |