Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1108 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 1108 conjugacy classes of subgroups — too many to draw. Only its 200 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×#88788 | C2 | semidirect |
| 3. C3×C4×C3⋊(C3⋊C8) | C2 | semidirect |
| 4. C32×C4⋊(C3⋊C8) | C2 | semidirect |
| 5. #11722024 | C2 | semidirect |
| 24. C4×C3⋊(C3⋊C8) | D3 | semidirect |
| 25. C3×C4⋊(C3⋊C8) | D3 | semidirect |
| 37. C3×C3⋊(C3⋊C8) | D4 | semidirect |
| 69. C33×C4 | M16 | semidirect |
| 82. C4⋊(C3⋊C8) | C3⋊D3 | semidirect |
| 110. C3⋊(C3⋊C8) | D12 | semidirect |
| 160. C32×C4 | ΓL(1,𝔽25) | semidirect |
| 161. C32×C4 | ΓL(1,𝔽25) | semidirect |
| 174. C33 | #436 | semidirect |
| 244. C3×C4 | #3712 | semidirect |
| 245. C3×C4 | #3743 | semidirect |
| 254. C32 | #4688 | semidirect |
| 255. C32 | #4838 | semidirect |
| 285. C4 | #88788 | semidirect |
| 289. C3 | #10590338 | semidirect |
| 290. C3 | #10592537 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C4⋊(C3⋊(C3⋊D3)) | 2 |
| C2×#88788 | 2 |
| C3×C4×C3⋊(C3⋊C8) | 2 |
| C32×C4⋊(C3⋊C8) | 2 |
| #11722024 | 2 |
| #10592537 | 3 |
| #10590338 | 3 |