Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
488 conjugacy classes of subgroups; only the 244 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 244 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32×C9 | A4 |
| commutator, hypocenter | C22 | C2×C32×C27 |
| Frattini | C9 | C2×C32×A4 |
| Fitting | C23×C32×C9 | C3 |
| socle, prime radical | C23×C33 | C9 |
| cosocle | C22×C9 | C2×C33 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C2×C32×C9 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C32×C22⋊C27 | C2 | direct (N × H) |
| 3. C2×C3×C22⋊C27 | C3 | direct (N × H) |
| 8. C3×C22⋊C27 | C2×C3 | direct (N × H) |
| 13. C2×C22⋊C27 | C32 | direct (N × H) |
| 27. C22⋊C27 | C2×C32 | direct (N × H) |
| 30. C23×C32 | C27 | semidirect |
| 48. C22×C32 | C2×C27 | semidirect |
| 60. C23×C3 | C3×C27 | semidirect |
| 66. C2×C32 | C22⋊C27 | direct (N × H) |
| 78. C22×C3 | C2×C3×C27 | semidirect |
| 80. C32 | C2×C22⋊C27 | direct (N × H) |
| 84. C23 | C32×C27 | semidirect |
| 89. C2×C3 | C3×C22⋊C27 | direct (N × H) |
| 93. C22 | C2×C32×C27 | semidirect |
| 94. C3 | C2×C3×C22⋊C27 | direct (N × H) |
| 98. C2 | C32×C22⋊C27 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C22⋊C27 | 2 |
| C23×C32×C9 | 3 |
| C2×C3×C22⋊C27 | 3 |
| C2×C32×C27 | 4 |