Finite Group DatabasebetaFinite Group DatabasebetaOrder 2592.
348 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 76 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×C9 | A42 |
| commutator, hypocenter | H(5,𝔽2) | C32×C9 |
| Frattini, socle | C2×C3 | C3×A42 |
| Fitting | C9×H(5,𝔽2) | C32 |
| prime radical | C3×Ω+(4,𝔽3) | C3 |
| cosocle | C3×H(5,𝔽2) | C33 |
| LCS | G ▷ H(5,𝔽2) | |
| UCS | C1 ◁ C2×C9 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C9×#997 | C3 | semidirect |
| 3. C9×#994 | C3 | semidirect |
| 4. #997⋊C9 | C3 | semidirect |
| 5. SL(2,𝔽3)⋊(C22⋊C9) | C3 | semidirect |
| 10. Ω+(4,𝔽3) | C9 | direct (N × H) |
| 11. C9×H(5,𝔽2) | C32 | semidirect |
| 12. #63703 | C32 | semidirect |
| 13. #63700 | C32 | semidirect |
| 21. C9×SL(2,𝔽3) | A4 | semidirect |
| 30. #997 | C3×C9 | semidirect |
| 31. #994 | C3×C9 | semidirect |
| 61. H(5,𝔽2) | C32×C9 | semidirect |
| 74. SL(2,𝔽3) | C9×A4 | semidirect |
| 94. C9 | Ω+(4,𝔽3) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Ω+(4,𝔽3) | 3 |
| C9×#997 | 3 |
| C9×#994 | 3 |
| #997⋊C9 | 3 |
| SL(2,𝔽3)⋊(C22⋊C9) | 3 |
| C3×C9×SL(2,𝔽3) | 4 |