Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1782 conjugacy classes of subgroups; only the 799 normal subgroups are shown.
This group has 1782 conjugacy classes of subgroups — too many to draw. Only its 799 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C2×C4×PSU(3,𝔽2) | C2 | direct (N × H) |
| 7. C22×PSU(3,𝔽2) | C4 | direct (N × H) |
| 12. C4×PSU(3,𝔽2) | C22 | direct (N × H) |
| 18. C2×PSU(3,𝔽2) | C2×C4 | direct (N × H) |
| 20. C22×C32×C4 | Q8 | semidirect |
| 21. C22×C3⋊Dic3 | Q8 | semidirect |
| 22. C2×C4×C3⋊D3 | Q8 | semidirect |
| 37. PSU(3,𝔽2) | C22×C4 | direct (N × H) |
| 38. C2×C32×C4 | C2×Q8 | semidirect |
| 39. C2×C3⋊Dic3 | C2×Q8 | semidirect |
| 40. C4×C3⋊D3 | C2×Q8 | semidirect |
| 51. C22×C32 | C4×Q8 | semidirect |
| 53. C2×C3⋊D3 | C4×Q8 | semidirect |
| 60. C32×C4 | C22×Q8 | semidirect |
| 61. C3⋊Dic3 | C22×Q8 | semidirect |
| 79. C2×C32 | C2×C4×Q8 | semidirect |
| 81. C3⋊D3 | C2×C4×Q8 | semidirect |
| 94. C22×C4 | PSU(3,𝔽2) | direct (N × H) |
| 106. C32 | C22×C4×Q8 | semidirect |
| 120. C2×C4 | C2×PSU(3,𝔽2) | direct (N × H) |
| 131. C22 | C4×PSU(3,𝔽2) | direct (N × H) |
| 136. C4 | C22×PSU(3,𝔽2) | direct (N × H) |
| 141. C2 | C2×C4×PSU(3,𝔽2) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×PSU(3,𝔽2) | 2 |
| C22×C4×#157 | 2 |
| C22×#3777 | 2 |
| C2×C4×PSU(3,𝔽2) | 2 |
| C22×C4×Q8 | 9 |