Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
354 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 57 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. C2×#89092 | C2 | semidirect |
| 2. C3×C4⋊PSU(3,𝔽2) | C2 | semidirect |
| 4. C4×C3⋊AGL(1,𝔽9) | C2 | semidirect |
| 16. C4⋊PSU(3,𝔽2) | D3 | semidirect |
| 26. C3⋊AGL(1,𝔽9) | D4 | semidirect |
| 46. C3×#157 | SD16 | semidirect |
| 48. C33×C4 | SD16 | semidirect |
| 49. C3×C3⋊Dic3 | SD16 | semidirect |
| 97. #157 | #215 | semidirect |
| 101. C32×C4 | #215 | semidirect |
| 102. C3⋊Dic3 | #215 | semidirect |
| 108. C33 | #492 | semidirect |
| 162. C3×C4 | AΓL(1,𝔽9) | semidirect |
| 166. C32 | #5085 | semidirect |
| 197. C4 | #89092 | semidirect |
| 200. C3 | #10596408 | 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 |
| #11724344 | 2 |
| C4×C3⋊AGL(1,𝔽9) | 2 |
| #10596408 | 3 |
| #5085 | 9 |