Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
392 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 70 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 |
|---|---|---|
| 1. C3×Q8×H(3,𝔽3) | C2 | semidirect |
| 3. C3×#6180 | C2 | semidirect |
| 5. #88549 | C3 | direct (N × H) |
| 9. C33×Q8 | D3 | semidirect |
| 13. Q8×H(3,𝔽3) | C2×C3 | semidirect |
| 15. #6180 | C2×C3 | semidirect |
| 29. C3×H(3,𝔽3) | SD16 | semidirect |
| 32. C32×Q8 | C3×D3 | semidirect |
| 59. C33 | #215 | semidirect |
| 61. H(3,𝔽3) | C3×SD16 | semidirect |
| 64. C3×Q8 | #272 | semidirect |
| 93. C32 | C3×#215 | semidirect |
| 95. Q8 | C3×#272 | semidirect |
| 110. C3 | #88549 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Q8×H(3,𝔽3) | 2 |
| C3×C4⋊#272 | 2 |
| C3×#6180 | 2 |
| C32×#215 | 3 |
| #88549 | 3 |