Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
310 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 51 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×C4⋊PSU(3,𝔽2) | C2 | semidirect |
| 4. C4⋊(C3⋊AGL(1,𝔽9)) | C2 | semidirect |
| 5. #11724102 | C2 | semidirect |
| 18. C4⋊PSU(3,𝔽2) | D3 | semidirect |
| 55. C33×C4 | SD16 | semidirect |
| 57. C3×C3⋊Dic3 | SD16 | semidirect |
| 116. C32×C4 | #215 | semidirect |
| 118. C3⋊Dic3 | #215 | semidirect |
| 128. C33 | #461 | semidirect |
| 189. C3×C4 | AΓL(1,𝔽9) | semidirect |
| 196. C32 | #5083 | semidirect |
| 231. C4 | #89092 | semidirect |
| 234. C3 | #10596409 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89092 | 2 |
| C3×C4⋊PSU(3,𝔽2) | 2 |
| C4×#157⋊D3 | 2 |
| C4⋊(C3⋊AGL(1,𝔽9)) | 2 |
| #11724102 | 2 |
| #10596409 | 3 |
| #5083 | 9 |