Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
190 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 47 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 |
|---|---|---|
| 20. C33×Q8 | C8 | semidirect |
| 24. C3×#634 | C8 | semidirect |
| 53. C32×Q8 | C3⋊C8 | semidirect |
| 57. #634 | C3⋊C8 | semidirect |
| 93. C33 | Q8⋊C8 | semidirect |
| 98. C3×Q8 | AGL(1,𝔽9) | semidirect |
| 142. C32 | #4535 | semidirect |
| 145. Q8 | C3⋊AGL(1,𝔽9) | semidirect |
| 171. C3 | Q8⋊AGL(1,𝔽9) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Q8×#157 | 2 |
| C4⋊(C3⋊AGL(1,𝔽9)) | 2 |
| C4×C3⋊AGL(1,𝔽9) | 2 |
| Q8⋊AGL(1,𝔽9) | 3 |
| #4535 | 9 |