Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
4224 conjugacy classes of subgroups; only the 2328 normal subgroups are shown.
This group has 4224 conjugacy classes of subgroups — too many to draw. Only its 2328 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C32 | C24 |
| commutator, Frattini, cosocle | C22 | C25×C32 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C32 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C32×H(3,𝔽4) | C2 | direct (N × H) |
| 2. C2×C32×#124 | C2 | semidirect |
| 3. C2×C32×#120 | C2 | semidirect |
| 4. C2×C3×H(3,𝔽4) | C3 | direct (N × H) |
| 5. C25×C32 | C22 | semidirect |
| 6. C22×C32×Q8 | C22 | semidirect |
| 8. C32×#124 | C22 | semidirect |
| 9. C32×#120 | C22 | semidirect |
| 10. C2×C32×C22⋊C4 | C22 | semidirect |
| 11. C2×C32×C42 | C22 | semidirect |
| 12. C3×H(3,𝔽4) | C2×C3 | direct (N × H) |
| 13. C2×C3×#124 | C2×C3 | semidirect |
| 14. C2×C3×#120 | C2×C3 | semidirect |
| 17. C24×C32 | C23 | semidirect |
| 19. C2×C32×Q8 | C23 | semidirect |
| 23. C32×C22⋊C4 | C23 | semidirect |
| 24. C32×C42 | C23 | semidirect |
| 25. C2×H(3,𝔽4) | C32 | direct (N × H) |
| 26. C25×C3 | C22×C3 | semidirect |
| 27. C22×C3×Q8 | C22×C3 | semidirect |
| 29. C3×#124 | C22×C3 | semidirect |
| 30. C3×#120 | C22×C3 | semidirect |
| 31. C2×C3×C22⋊C4 | C22×C3 | semidirect |
| 32. C2×C3×C42 | C22×C3 | semidirect |
| 42. H(3,𝔽4) | C2×C32 | direct (N × H) |
| 43. C2×#124 | C2×C32 | semidirect |
| 44. C2×#120 | C2×C32 | semidirect |
| 47. C24×C3 | C23×C3 | semidirect |
| 49. C2×C3×Q8 | C23×C3 | semidirect |
| 53. C3×C22⋊C4 | C23×C3 | semidirect |
| 54. C3×C42 | C23×C3 | semidirect |
| 61. C25 | C22×C32 | semidirect |
| 62. C22×Q8 | C22×C32 | semidirect |
| 64. #124 | C22×C32 | semidirect |
| 65. #120 | C22×C32 | semidirect |
| 66. C2×C22⋊C4 | C22×C32 | semidirect |
| 67. C2×C42 | C22×C32 | semidirect |
| 78. C2×C32 | H(3,𝔽4) | direct (N × H) |
| 82. C24 | C23×C32 | semidirect |
| 84. C2×Q8 | C23×C32 | semidirect |
| 88. C22⋊C4 | C23×C32 | semidirect |
| 89. C42 | C23×C32 | semidirect |
| 96. C32 | C2×H(3,𝔽4) | direct (N × H) |
| 107. C2×C3 | C3×H(3,𝔽4) | direct (N × H) |
| 115. C3 | C2×C3×H(3,𝔽4) | direct (N × H) |
| 117. C2 | C32×H(3,𝔽4) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×H(3,𝔽4) | 2 |
| C2×C32×#124 | 2 |
| C2×C32×#120 | 2 |
| C2×C3×H(3,𝔽4) | 3 |