Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1028 conjugacy classes of subgroups; only the 180 normal subgroups are shown.
This group has 1028 conjugacy classes of subgroups — too many to draw. Only its 180 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. Q8×C3⋊#157 | C2 | semidirect |
| 3. C3×Q8×#157 | C2 | semidirect |
| 4. #11724259 | C2 | semidirect |
| 5. D12×#157 | C2 | semidirect |
| 6. C4×D3×#157 | C2 | semidirect |
| 7. #11724247 | C2 | semidirect |
| 11. #89080 | C4 | semidirect |
| 13. C32×#239 | C4 | semidirect |
| 16. #89022 | C4 | semidirect |
| 17. #89015 | C4 | semidirect |
| 28. Q8×#157 | D3 | semidirect |
| 40. C33×Q8 | C2×C4 | semidirect |
| 41. C4⋊(C3⋊(C3⋊D3)) | C2×C4 | semidirect |
| 42. C4×C3⋊(C3⋊D3) | C2×C4 | semidirect |
| 44. C3×#634 | C2×C4 | semidirect |
| 45. C32×D12 | C2×C4 | semidirect |
| 46. C32×C4×D3 | C2×C4 | semidirect |
| 47. #6291 | C2×C4 | semidirect |
| 48. #6289 | C2×C4 | semidirect |
| 50. D3×C3⋊Dic3 | C2×C4 | semidirect |
| 82. C3⋊#157 | #41 | semidirect |
| 84. C3×#157 | #41 | semidirect |
| 107. C32×Q8 | C4×D3 | semidirect |
| 121. #634 | C4×D3 | semidirect |
| 143. #239 | #157 | direct (N × H) |
| 174. #157 | #239 | direct (N × H) |
| 192. C33 | C4×#41 | semidirect |
| 198. C3×Q8 | C2×#157 | semidirect |
| 213. D12 | C2×#157 | semidirect |
| 224. C4×D3 | C2×#157 | semidirect |
| 281. C32 | C4×#239 | semidirect |
| 284. Q8 | D3×#157 | semidirect |
| 327. C3 | #41×#157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3⋊D3×#239 | 2 |
| Q8×C3⋊#157 | 2 |
| C3×Q8×#157 | 2 |
| #11724259 | 2 |
| D12×#157 | 2 |
| C4×D3×#157 | 2 |
| #11724247 | 2 |
| #41×#157 | 3 |
| C4×#239 | 9 |