Finite Group DatabasebetaFinite Group DatabasebetaOrder 2592.
4690 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 4690 conjugacy classes of subgroups — too many to draw. Only its 232 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C24×C33 | C2×C3 |
| LCS | G ▷ C24×C33 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C33×C22⋊A4 | C2 | semidirect |
| 2. C24×C3⋊(C3⋊D3) | C3 | semidirect |
| 5. C24×C33 | C2×C3 | semidirect |
| 9. C32×C22⋊A4 | D3 | semidirect |
| 17. C22×C3⋊(C3⋊D3) | A4 | semidirect |
| 20. C24×C32 | C3×D3 | semidirect |
| 24. C3×C22⋊A4 | C3⋊D3 | semidirect |
| 26. C22×C33 | C2×A4 | semidirect |
| 43. C3⋊(C3⋊D3) | C22⋊A4 | direct (N × H) |
| 45. C24×C3 | C3×C3⋊D3 | semidirect |
| 49. C22⋊A4 | C3⋊(C3⋊D3) | direct (N × H) |
| 51. C22×C32 | D3×A4 | semidirect |
| 60. C33 | C2×C22⋊A4 | semidirect |
| 73. C24 | C3×C3⋊(C3⋊D3) | semidirect |
| 75. C22×C3 | A4×C3⋊D3 | semidirect |
| 83. C32 | D3×C22⋊A4 | semidirect |
| 97. C22 | A4×C3⋊(C3⋊D3) | semidirect |
| 100. C3 | C3⋊D3×C22⋊A4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×C22⋊A4 | 2 |
| C24×C3⋊(C3⋊D3) | 3 |
| C3⋊D3×C22⋊A4 | 3 |
| A4×C3⋊(C3⋊D3) | 4 |