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. C22×C33×D4 | C2 | semidirect |
| 2. C22×#6312 | C2 | semidirect |
| 3. C23×C3⋊(C3⋊Dic3) | C2 | semidirect |
| 4. C2×#89078 | C2 | direct (N × H) |
| 5. C22×C4×C3⋊(C3⋊D3) | C2 | semidirect |
| 6. C22×#6308 | C2 | semidirect |
| 10. C2×C33×D4 | C22 | semidirect |
| 12. C2×#6312 | C22 | semidirect |
| 15. C22×C3⋊(C3⋊Dic3) | C22 | semidirect |
| 16. #89078 | C22 | direct (N × H) |
| 17. C2×C4×C3⋊(C3⋊D3) | C22 | semidirect |
| 18. C2×#6308 | C22 | semidirect |
| 19. C22×C32×D4 | D3 | semidirect |
| 30. C33×D4 | C23 | semidirect |
| 32. #6312 | C23 | semidirect |
| 35. C2×C3⋊(C3⋊Dic3) | C23 | semidirect |
| 36. C4×C3⋊(C3⋊D3) | C23 | semidirect |
| 37. #6308 | C23 | semidirect |
| 41. C2×C32×D4 | C2×D3 | semidirect |
| 51. C22×C33 | #41 | semidirect |
| 59. C22×C3×D4 | C3⋊D3 | semidirect |
| 70. C32×D4 | C22×D3 | semidirect |
| 80. C2×C33 | C2×#41 | semidirect |
| 85. C2×C3×D4 | C2×C3⋊D3 | semidirect |
| 95. C22×C32 | #237 | semidirect |
| 106. C22×D4 | C3⋊(C3⋊D3) | semidirect |
| 109. C33 | C22×#41 | semidirect |
| 115. C3×D4 | C22×C3⋊D3 | semidirect |
| 124. C2×C32 | C2×#237 | semidirect |
| 132. C2×D4 | C2×C3⋊(C3⋊D3) | semidirect |
| 139. C22×C3 | #3830 | semidirect |
| 147. C32 | C22×#237 | semidirect |
| 155. D4 | C22×C3⋊(C3⋊D3) | semidirect |
| 162. C2×C3 | C2×#3830 | semidirect |
| 168. C22 | #89078 | direct (N × H) |
| 174. C3 | C22×#3830 | semidirect |
| 177. C2 | C2×#89078 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C33×D4 | 2 |
| C22×#6312 | 2 |
| C23×C3⋊(C3⋊Dic3) | 2 |
| C2×#89078 | 2 |
| C22×C4×C3⋊(C3⋊D3) | 2 |
| C22×#6308 | 2 |
| C22×#3830 | 3 |