Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1372 conjugacy classes of subgroups; only the 403 normal subgroups are shown.
This group has 1372 conjugacy classes of subgroups — too many to draw. Only its 403 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. C2×C33×D8 | C2 | semidirect |
| 2. C2×#88852 | C2 | semidirect |
| 3. #11722196 | C2 | direct (N × H) |
| 4. C2×C3⋊(C3⋊(C3⋊C16)) | C2 | semidirect |
| 9. C33×D8 | C22 | semidirect |
| 12. #88852 | C22 | semidirect |
| 13. C3⋊(C3⋊(C3⋊C16)) | C22 | semidirect |
| 14. C2×C32×D8 | D3 | semidirect |
| 31. C32×D8 | C2×D3 | semidirect |
| 43. C2×C3×D8 | C3⋊D3 | semidirect |
| 58. C2×C33 | D16 | semidirect |
| 64. C3×D8 | C2×C3⋊D3 | semidirect |
| 77. C2×D8 | C3⋊(C3⋊D3) | semidirect |
| 80. C33 | C2×D16 | semidirect |
| 91. C2×C32 | #826 | semidirect |
| 99. D8 | C2×C3⋊(C3⋊D3) | semidirect |
| 109. C32 | C2×#826 | semidirect |
| 120. C2×C3 | #63653 | semidirect |
| 130. C3 | C2×#63653 | semidirect |
| 133. C2 | #11722196 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×D8 | 2 |
| C2×#88852 | 2 |
| #11722196 | 2 |
| C2×C3⋊(C3⋊(C3⋊C16)) | 2 |
| C2×#63653 | 3 |