Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
908 conjugacy classes of subgroups; only the 206 normal subgroups are shown.
This group has 908 conjugacy classes of subgroups — too many to draw. Only its 206 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. C2×#88787 | C2 | semidirect |
| 3. C4×C3⋊(C3⋊(C3⋊C8)) | C2 | semidirect |
| 4. C32×C4⋊(C3⋊C8) | C2 | semidirect |
| 5. #11722023 | C2 | semidirect |
| 26. C3×C4⋊(C3⋊C8) | D3 | semidirect |
| 37. C3⋊(C3⋊(C3⋊C8)) | D4 | semidirect |
| 67. C33×C4 | M16 | semidirect |
| 78. C4⋊(C3⋊C8) | C3⋊D3 | semidirect |
| 150. C32×C4 | ΓL(1,𝔽25) | semidirect |
| 151. C32×C4 | #208 | semidirect |
| 163. C33 | #436 | semidirect |
| 227. C3×C4 | #3711 | semidirect |
| 228. C3×C4 | #3743 | semidirect |
| 235. C32 | #4838 | semidirect |
| 236. C32 | #5012 | semidirect |
| 265. C4 | #88787 | semidirect |
| 269. C3 | #10590339 | semidirect |
| 270. C3 | #10592537 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×C4⋊(C3⋊D3) | 2 |
| C2×#88787 | 2 |
| C4×C3⋊(C3⋊(C3⋊C8)) | 2 |
| C32×C4⋊(C3⋊C8) | 2 |
| #11722023 | 2 |
| #10592537 | 3 |
| #10590339 | 3 |