Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
356 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 77 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. Dic6×H(3,𝔽3) | C2 | semidirect |
| 3. C3⋊C8×H(3,𝔽3) | C2 | semidirect |
| 4. C32×#214 | C3 | semidirect |
| 10. C32×Dic6 | C2×C3 | semidirect |
| 11. C32×C3⋊C8 | C2×C3 | semidirect |
| 29. C3×H(3,𝔽3) | SD16 | semidirect |
| 49. #214 | H(3,𝔽3) | direct (N × H) |
| 63. C33 | C3×SD16 | semidirect |
| 65. H(3,𝔽3) | #214 | direct (N × H) |
| 73. Dic6 | C2×H(3,𝔽3) | semidirect |
| 76. C3⋊C8 | C2×H(3,𝔽3) | semidirect |
| 104. C32 | C3×#214 | semidirect |
| 125. C3 | SD16×H(3,𝔽3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D4×H(3,𝔽3) | 2 |
| Dic6×H(3,𝔽3) | 2 |
| C3⋊C8×H(3,𝔽3) | 2 |
| C32×#214 | 3 |
| SD16×H(3,𝔽3) | 3 |