Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2268 conjugacy classes of subgroups; only the 427 normal subgroups are shown.
This group has 2268 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 |
|---|---|---|
| 4. C33×#103 | C2 | semidirect |
| 5. #11722205 | C2 | semidirect |
| 6. #11722186 | C2 | semidirect |
| 7. #11722180 | C2 | semidirect |
| 11. Q8×C3⋊(C3⋊D3) | C4 | semidirect |
| 26. C32×#103 | D3 | semidirect |
| 32. C33×Q8 | C2×C4 | semidirect |
| 45. #6308 | C2×C4 | semidirect |
| 77. C3×#103 | C3⋊D3 | semidirect |
| 83. C32×Q8 | C4×D3 | semidirect |
| 103. C3⋊(C3⋊D3) | #103 | direct (N × H) |
| 135. #103 | C3⋊(C3⋊D3) | direct (N × H) |
| 136. C33 | C2×#103 | semidirect |
| 139. C3×Q8 | C4×C3⋊D3 | semidirect |
| 184. C32 | D3×#103 | semidirect |
| 190. Q8 | C4×C3⋊(C3⋊D3) | semidirect |
| 218. C3 | C3⋊D3×#103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×C3⋊(C3⋊D3) | 2 |
| C2×C8×C3⋊(C3⋊D3) | 2 |
| C4⋊C4×C3⋊(C3⋊D3) | 2 |
| C33×#103 | 2 |
| #11722205 | 2 |
| #11722186 | 2 |
| #11722180 | 2 |
| C3⋊D3×#103 | 3 |