Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1028 conjugacy classes of subgroups; only the 280 normal subgroups are shown.
This group has 1028 conjugacy classes of subgroups — too many to draw. Only its 280 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 |
|---|---|---|
| 3. C4×C3⋊(C3⋊(C3⋊C8)) | C2 | semidirect |
| 4. C32×C4×C3⋊C8 | C2 | semidirect |
| 5. #11722020 | C2 | semidirect |
| 15. #88787 | C4 | direct (N × H) |
| 25. C3×C4×C3⋊C8 | D3 | semidirect |
| 34. C3⋊(C3⋊(C3⋊C8)) | C2×C4 | semidirect |
| 35. C32×C3⋊C8 | C2×C4 | semidirect |
| 59. C33×C4 | M16 | semidirect |
| 73. C4×C3⋊C8 | C3⋊D3 | semidirect |
| 94. C3×C3⋊C8 | C4×D3 | semidirect |
| 126. C32×C4 | ΓL(1,𝔽25) | semidirect |
| 127. C32×C4 | #208 | semidirect |
| 139. C33 | C4×M16 | semidirect |
| 160. C3⋊C8 | C4×C3⋊D3 | semidirect |
| 188. C3×C4 | #3711 | semidirect |
| 189. C3×C4 | #3743 | semidirect |
| 195. C32 | C4×ΓL(1,𝔽25) | semidirect |
| 196. C32 | C4×#208 | semidirect |
| 219. C4 | #88787 | direct (N × H) |
| 222. C3 | C4×#3711 | semidirect |
| 223. C3 | C4×#3743 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C42×C3⋊D3 | 2 |
| C2×#88787 | 2 |
| C4×C3⋊(C3⋊(C3⋊C8)) | 2 |
| C32×C4×C3⋊C8 | 2 |
| #11722020 | 2 |
| C4×#3743 | 3 |
| C4×#3711 | 3 |