Finite Group DatabasebetaFinite Group DatabasebetaOrder 2592.
3829 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 3829 conjugacy classes of subgroups — too many to draw. Only its 84 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, Fitting, cosocle, hypocenter | C24×C33 | C2×C3 |
| Frattini | C3 | C3⋊D3×C22⋊A4 |
| socle | C24×C32 | C3×D3 |
| LCS | G ▷ C24×C33 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C32⋊(C22⋊A4) | C2 | semidirect |
| 2. C24×C3⋊(C3⋊D3) | C3 | semidirect |
| 6. C24×C33 | C2×C3 | semidirect |
| 10. C32×C22⋊A4 | D3 | semidirect |
| 12. C32⋊(C22⋊A4) | D3 | semidirect |
| 23. C22×C3⋊(C3⋊D3) | A4 | semidirect |
| 29. C24×C32 | C3×D3 | semidirect |
| 40. C3×C22⋊A4 | C3⋊D3 | semidirect |
| 42. C22×C33 | C2×A4 | semidirect |
| 74. C3⋊(C3⋊D3) | C22⋊A4 | semidirect |
| 78. C24×C3 | (C3⋊D3)⋊C3 | semidirect |
| 94. C22×C32 | D3×A4 | semidirect |
| 112. C33 | C2×C22⋊A4 | semidirect |
| 144. C24 | C3⋊((C3⋊D3)⋊C3) | semidirect |
| 149. C22×C3 | (C3⋊D3)⋊A4 | semidirect |
| 170. C32 | D3×C22⋊A4 | semidirect |
| 190. C22 | C3⋊((C3⋊D3)⋊A4) | semidirect |
| 195. 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 |
|---|---|
| C3×C32⋊(C22⋊A4) | 2 |
| C24×C3⋊(C3⋊D3) | 3 |
| C3⋊D3×C22⋊A4 | 3 |
| (C3⋊D3)⋊(C22⋊A4) | 3 |
| C3⋊((C3⋊D3)⋊A4) | 4 |