Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
330 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×A4×C27 | C2 |
| Frattini | C9 | C3⋊(C3⋊S4) |
| Fitting | C22×C3×C27 | D3 |
| socle | C22×C32 | C3⋊D9 |
| LCS | G ▷ C3×A4×C27 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×A4×C27 | C2 | semidirect |
| 8. C22×C3×C27 | D3 | semidirect |
| 10. C3×C22⋊C27 | D3 | semidirect |
| 11. A4×C27 | D3 | semidirect |
| 33. C22×C27 | C3⋊D3 | semidirect |
| 35. C22⋊C27 | C3⋊D3 | semidirect |
| 40. C3×C27 | S4 | semidirect |
| 58. C3×A4 | D27 | semidirect |
| 74. C27 | C3⋊S4 | semidirect |
| 87. C22×C3 | C3⋊D27 | semidirect |
| 91. A4 | C3⋊D27 | semidirect |
| 107. C22 | C3⋊(C3⋊D27) | semidirect |
| 110. C3 | A4⋊D27 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×A4×C27 | 2 |
| C3⋊(C9⋊S4) | 3 |
| C3⋊((C22⋊C27)⋊C2) | 3 |
| A4⋊D27 | 3 |
| #10619677 | 3 |
| C3⋊(C3⋊D27) | 4 |