Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
254 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
|---|---|---|
| 4. Q8×AGL(1,𝔽9) | C3 | direct (N × H) |
| 16. C3×AGL(1,𝔽9) | Q8 | direct (N × H) |
| 17. C33×Q8 | C8 | semidirect |
| 19. C3×#634 | C8 | semidirect |
| 39. AGL(1,𝔽9) | C3×Q8 | direct (N × H) |
| 42. C32×Q8 | C3×C8 | semidirect |
| 44. #634 | C3×C8 | semidirect |
| 70. C33 | C8×Q8 | semidirect |
| 74. C3×Q8 | AGL(1,𝔽9) | direct (N × H) |
| 106. C32 | C3×C8×Q8 | semidirect |
| 108. Q8 | C3×AGL(1,𝔽9) | direct (N × H) |
| 129. C3 | Q8×AGL(1,𝔽9) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Q8×#157 | 2 |
| C3×C4⋊AGL(1,𝔽9) | 2 |
| C3×C4×AGL(1,𝔽9) | 2 |
| Q8×AGL(1,𝔽9) | 3 |
| C3×C8×Q8 | 9 |