Finite Group DatabasebetaFinite Group DatabasebetaOrder 2592.
510 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 39 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 | C2 | #13049783 |
| commutator | C32×C3⋊D3 | C42 |
| Fitting, socle | C2×C34 | C4⋊C4 |
| prime radical, cosocle | C2×C3⋊D32 | C22 |
| hypocenter | C34 | #95 |
| LCS | G ▷ C32×C3⋊D3 ▷ C34 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. C2×C3⋊(C3⋊#157) | C4 | semidirect |
| 6. C2×C32×#157 | C4 | semidirect |
| 8. #10620198 | C4 | semidirect |
| 48. C34 | #95 | semidirect |
| 61. C2×#157 | #157 | semidirect |
| 157. C32 | #63747 | semidirect |
| 158. C32 | #63781 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10620198 | 2 |
| C2×C3⋊D3×#157 | 2 |
| #63781 | 9 |
| #63747 | 9 |