Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2128 conjugacy classes of subgroups; only the 351 normal subgroups are shown.
This group has 2128 conjugacy classes of subgroups — too many to draw. Only its 351 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. C33×#137 | C2 | semidirect |
| 3. #11723988 | C2 | semidirect |
| 4. #11723983 | C2 | semidirect |
| 5. #11722207 | C2 | semidirect |
| 6. #11722195 | C2 | semidirect |
| 7. #11722193 | C2 | semidirect |
| 10. C2×C33×Q8 | C22 | semidirect |
| 20. C33×M16 | C22 | semidirect |
| 24. C4×C3⋊(C3⋊Dic3) | C22 | semidirect |
| 25. #88855 | C22 | semidirect |
| 27. C32×#137 | D3 | semidirect |
| 57. C2×C32×Q8 | C2×D3 | semidirect |
| 67. C32×M16 | C2×D3 | semidirect |
| 86. C3×#137 | C3⋊D3 | semidirect |
| 121. C2×C3×Q8 | C2×C3⋊D3 | semidirect |
| 131. C3×M16 | C2×C3⋊D3 | semidirect |
| 151. #137 | C3⋊(C3⋊D3) | semidirect |
| 156. C33 | #455 | semidirect |
| 188. C2×Q8 | C2×C3⋊(C3⋊D3) | semidirect |
| 198. M16 | C2×C3⋊(C3⋊D3) | semidirect |
| 213. C32 | #5202 | semidirect |
| 253. C3 | #10592901 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11724684 | 2 |
| C33×#137 | 2 |
| #11723988 | 2 |
| #11723983 | 2 |
| #11722207 | 2 |
| #11722195 | 2 |
| #11722193 | 2 |
| #10592901 | 3 |