Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
996 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 996 conjugacy classes of subgroups — too many to draw. Only its 174 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. D3×C4⋊#157 | C2 | semidirect |
| 7. #11724246 | C2 | semidirect |
| 10. #89080 | C4 | semidirect |
| 12. C32×#239 | C4 | semidirect |
| 15. #89022 | C4 | semidirect |
| 16. #89015 | C4 | semidirect |
| 28. Q8×#157 | D3 | semidirect |
| 39. C33×Q8 | C2×C4 | semidirect |
| 40. C4⋊(C3⋊(C3⋊D3)) | C2×C4 | semidirect |
| 41. C4×C3⋊(C3⋊D3) | C2×C4 | semidirect |
| 43. C3×#634 | C2×C4 | semidirect |
| 44. C32×D12 | C2×C4 | semidirect |
| 45. C32×C4×D3 | C2×C4 | semidirect |
| 46. #6291 | C2×C4 | semidirect |
| 47. #6289 | C2×C4 | semidirect |
| 49. D3×C3⋊Dic3 | C2×C4 | semidirect |
| 105. C32×Q8 | C4×D3 | semidirect |
| 119. #634 | C4×D3 | semidirect |
| 141. #239 | #157 | semidirect |
| 190. C33 | #520 | semidirect |
| 196. C3×Q8 | C2×#157 | semidirect |
| 211. D12 | C2×#157 | semidirect |
| 221. C4×D3 | C2×#157 | semidirect |
| 278. C32 | #5574 | semidirect |
| 281. Q8 | D3×#157 | semidirect |
| 323. C3 | #10596650 | 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 |
| D3×C4⋊#157 | 2 |
| #11724246 | 2 |
| #10596650 | 3 |
| #5574 | 9 |