Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
12460 conjugacy classes of subgroups; only the 2491 normal subgroups are shown.
This group has 12460 conjugacy classes of subgroups — too many to draw. Only its 2491 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 |
|---|---|---|
| 1. C23×C33×C4 | C2 | semidirect |
| 2. C22×#6312 | C2 | semidirect |
| 3. C2×#89076 | C2 | direct (N × H) |
| 4. C22×C4⋊(C3⋊(C3⋊D3)) | C2 | semidirect |
| 5. C22×C4×C3⋊(C3⋊D3) | C2 | semidirect |
| 6. C22×#6308 | C2 | semidirect |
| 12. C22×C33×C4 | C22 | semidirect |
| 13. C2×#6312 | C22 | semidirect |
| 15. #89076 | C22 | direct (N × H) |
| 16. C2×C4⋊(C3⋊(C3⋊D3)) | C22 | semidirect |
| 17. C2×C4×C3⋊(C3⋊D3) | C22 | semidirect |
| 18. C2×#6308 | C22 | semidirect |
| 19. C23×C32×C4 | D3 | semidirect |
| 32. C2×C33×C4 | C23 | semidirect |
| 33. #6312 | C23 | semidirect |
| 35. C4⋊(C3⋊(C3⋊D3)) | C23 | semidirect |
| 36. C4×C3⋊(C3⋊D3) | C23 | semidirect |
| 37. #6308 | C23 | semidirect |
| 43. C22×C32×C4 | C2×D3 | semidirect |
| 51. C22×C33 | #41 | semidirect |
| 59. C23×C3×C4 | C3⋊D3 | semidirect |
| 72. C2×C32×C4 | C22×D3 | semidirect |
| 80. C2×C33 | C2×#41 | semidirect |
| 87. C22×C3×C4 | C2×C3⋊D3 | semidirect |
| 95. C22×C32 | #235 | semidirect |
| 108. C23×C4 | C3⋊(C3⋊D3) | semidirect |
| 109. C33 | C22×#41 | semidirect |
| 117. C2×C3×C4 | C22×C3⋊D3 | semidirect |
| 124. C2×C32 | C2×#235 | semidirect |
| 137. C22×C4 | C2×C3⋊(C3⋊D3) | semidirect |
| 139. C22×C3 | #3828 | semidirect |
| 147. C32 | C22×#235 | semidirect |
| 160. C2×C4 | C22×C3⋊(C3⋊D3) | semidirect |
| 162. C2×C3 | C2×#3828 | semidirect |
| 168. C22 | #89076 | direct (N × H) |
| 174. C3 | C22×#3828 | semidirect |
| 177. C2 | C2×#89076 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C33×C4 | 2 |
| C22×#6312 | 2 |
| C2×#89076 | 2 |
| C22×C4⋊(C3⋊(C3⋊D3)) | 2 |
| C22×C4×C3⋊(C3⋊D3) | 2 |
| C22×#6308 | 2 |
| C22×#3828 | 3 |