Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2632 conjugacy classes of subgroups; only the 409 normal subgroups are shown.
This group has 2632 conjugacy classes of subgroups — too many to draw. Only its 409 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. C2×C33×SD16 | C2 | semidirect |
| 3. #11723987 | C2 | semidirect |
| 4. C2×#88862 | C2 | semidirect |
| 5. #11722202 | C2 | semidirect |
| 6. #11722191 | C2 | semidirect |
| 7. #11722190 | C2 | semidirect |
| 10. C2×C33×Q8 | C22 | semidirect |
| 18. C2×C33×C8 | C22 | semidirect |
| 21. C4⋊(C3⋊(C3⋊Dic3)) | C22 | semidirect |
| 23. C2×C3⋊(C3⋊(C3⋊C8)) | C22 | semidirect |
| 25. C2×C32×SD16 | D3 | semidirect |
| 54. C2×C32×Q8 | C2×D3 | semidirect |
| 62. C2×C32×C8 | C2×D3 | semidirect |
| 78. C2×C3⋊(C3⋊D3) | SD16 | semidirect |
| 85. C2×C3×SD16 | C3⋊D3 | semidirect |
| 120. C2×C3×Q8 | C2×C3⋊D3 | semidirect |
| 128. C2×C3×C8 | C2×C3⋊D3 | semidirect |
| 152. C2×SD16 | C3⋊(C3⋊D3) | semidirect |
| 157. C33 | #450 | semidirect |
| 186. C2×Q8 | C2×C3⋊(C3⋊D3) | semidirect |
| 196. C2×C8 | C2×C3⋊(C3⋊D3) | semidirect |
| 216. C32 | #5169 | semidirect |
| 260. C3 | #10592868 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×C3⋊(C3⋊D3) | 2 |
| C2×C33×SD16 | 2 |
| #11723987 | 2 |
| C2×#88862 | 2 |
| #11722202 | 2 |
| #11722191 | 2 |
| #11722190 | 2 |
| #10592868 | 3 |