Finite Group DatabasebetaFinite Group DatabasebetaOrder 2592.
790 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 790 conjugacy classes of subgroups — too many to draw. Only its 120 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×C9×H(5,𝔽2) | C3 | semidirect |
| 3. C3×#63703 | C3 | semidirect |
| 4. C9×#997 | C3 | direct (N × H) |
| 11. C3×#997 | C9 | direct (N × H) |
| 13. C9×H(5,𝔽2) | C32 | semidirect |
| 14. #63703 | C32 | semidirect |
| 18. C23×C3×C9 | A4 | semidirect |
| 21. C3×Q8×C9 | A4 | semidirect |
| 38. C3×H(5,𝔽2) | C3×C9 | semidirect |
| 40. #997 | C3×C9 | direct (N × H) |
| 52. C23×C9 | C3×A4 | semidirect |
| 54. Q8×C9 | C3×A4 | semidirect |
| 78. H(5,𝔽2) | C32×C9 | semidirect |
| 82. C3×C9 | #997 | direct (N × H) |
| 85. C23×C3 | C9×A4 | semidirect |
| 88. C3×Q8 | C9×A4 | semidirect |
| 117. C9 | C3×#997 | direct (N × H) |
| 119. C23 | C3×C9×A4 | semidirect |
| 120. Q8 | C3×C9×A4 | semidirect |
| 133. C3 | C9×#997 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#997 | 3 |
| C3×C9×H(5,𝔽2) | 3 |
| C3×#63703 | 3 |
| C9×#997 | 3 |
| C2×C3×C9×A4 | 4 |
| C3×C9×SL(2,𝔽3) | 4 |