Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
1008 conjugacy classes of subgroups; only the 360 normal subgroups are shown.
This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 360 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C32×C4 | C33 |
| commutator | C32 | C2×C33×C4 |
| Frattini, cosocle | C2×C32 | C22×C33 |
| socle | C22×C32 | C2×C33 |
| prime radical | C22×C34 | C2×C3 |
| LCS | G ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C2×C32×C4 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×#6891 | C2 | direct (N × H) |
| 4. C2×C3×C4×3−1+2 | C3 | semidirect |
| 5. C2×C4×C32⋊C9 | C3 | semidirect |
| 6. C2×#6891 | C4 | direct (N × H) |
| 11. C3×C4×3−1+2 | C2×C3 | semidirect |
| 13. C4×C32⋊C9 | C2×C3 | semidirect |
| 14. #6891 | C2×C4 | direct (N × H) |
| 20. C2×C3×C4×C9 | C32 | semidirect |
| 23. C2×C3×3−1+2 | C3×C4 | semidirect |
| 25. C2×C32⋊C9 | C3×C4 | semidirect |
| 38. C3×C4×C9 | C2×C32 | semidirect |
| 40. C3×3−1+2 | C2×C3×C4 | semidirect |
| 41. C32⋊C9 | C2×C3×C4 | semidirect |
| 47. C2×C32×C4 | 3−1+2 | semidirect |
| 60. C2×C3×C9 | C32×C4 | semidirect |
| 74. C32×C4 | C2×3−1+2 | semidirect |
| 83. C3×C9 | C2×C32×C4 | semidirect |
| 97. C2×C32 | C4×3−1+2 | semidirect |
| 117. C32 | C2×C4×3−1+2 | semidirect |
| 120. C2×C4 | #6891 | direct (N × H) |
| 130. C4 | C2×#6891 | direct (N × H) |
| 135. C2 | C4×#6891 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6891 | 2 |
| C4×#6891 | 2 |
| C2×C34×C4 | 3 |
| C2×C3×C4×3−1+2 | 3 |
| C2×C4×C32⋊C9 | 3 |