Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1820 conjugacy classes of subgroups; only the 427 normal subgroups are shown.
This group has 1820 conjugacy classes of subgroups — too many to draw. Only its 427 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. C33×#106 | C2 | semidirect |
| 4. #11722187 | C2 | semidirect |
| 5. #11722178 | C2 | semidirect |
| 14. C8×C3⋊(C3⋊D3) | C4 | semidirect |
| 17. C32×#106 | D3 | semidirect |
| 28. C33×C8 | C2×C4 | semidirect |
| 29. C3⋊(C3⋊(C3⋊C8)) | C2×C4 | semidirect |
| 49. C3×#106 | C3⋊D3 | semidirect |
| 60. C32×C8 | C4×D3 | semidirect |
| 65. C3⋊(C3⋊D3) | #106 | direct (N × H) |
| 86. #106 | C3⋊(C3⋊D3) | direct (N × H) |
| 87. C33 | C2×#106 | semidirect |
| 96. C3×C8 | C4×C3⋊D3 | semidirect |
| 117. C32 | D3×#106 | semidirect |
| 127. C8 | C4×C3⋊(C3⋊D3) | semidirect |
| 139. C3 | C3⋊D3×#106 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×C3⋊(C3⋊D3) | 2 |
| C4⋊C4×C3⋊(C3⋊D3) | 2 |
| C33×#106 | 2 |
| #11722187 | 2 |
| #11722178 | 2 |
| C3⋊D3×#106 | 3 |