Finite Group DatabasebetaFinite Group DatabasebetaOrder 2592.
542 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 53 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 | #13049783 |
| commutator | C32×C3⋊D3 | C22×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C34 | C4⋊C4 |
| prime radical | C2×C3⋊D32 | C22 |
| cosocle | C3⋊D32 | C23 |
| hypocenter | C34 | C2×C4⋊C4 |
| LCS | G ▷ C32×C3⋊D3 ▷ C34 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #13049783 | C2 | direct (N × H) |
| 6. C2×C3⋊(C3⋊#157) | C4 | semidirect |
| 7. C2×C32×#157 | C4 | semidirect |
| 10. C3⋊D3×#157 | C4 | semidirect |
| 21. C3⋊(C3⋊#157) | C2×C4 | semidirect |
| 22. C32×#157 | C2×C4 | semidirect |
| 31. C2×C34 | C4⋊C4 | semidirect |
| 32. C3⋊(C3⋊(C3⋊D3)) | C4⋊C4 | semidirect |
| 34. C32×C3⋊D3 | C4⋊C4 | semidirect |
| 35. C32×C3⋊D3 | C4⋊C4 | semidirect |
| 61. C34 | C2×C4⋊C4 | semidirect |
| 75. C2×#157 | #157 | semidirect |
| 127. #157 | C2×#157 | semidirect |
| 149. C2×C32 | #3777 | semidirect |
| 150. C2×C32 | C4⋊#157 | semidirect |
| 165. C3⋊D3 | #3777 | semidirect |
| 166. C3⋊D3 | C4⋊#157 | semidirect |
| 198. C32 | C2×#3777 | semidirect |
| 199. C32 | C2×C4⋊#157 | semidirect |
| 244. C2 | #13049783 | direct (N × H) |
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 |
| #13049783 | 2 |
| C2×C4⋊#157 | 9 |
| C2×#3777 | 9 |