Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1260 conjugacy classes of subgroups; only the 403 normal subgroups are shown.
This group has 1260 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×Q16 | C2 | semidirect |
| 3. #11722198 | C2 | direct (N × H) |
| 4. C2×C3⋊(C3⋊(C3⋊C16)) | C2 | semidirect |
| 9. C33×Q16 | C22 | semidirect |
| 13. C3⋊(C3⋊(C3⋊C16)) | C22 | semidirect |
| 14. C2×C32×Q16 | D3 | semidirect |
| 31. C32×Q16 | C2×D3 | semidirect |
| 42. C2×C3×Q16 | C3⋊D3 | semidirect |
| 56. C2×C33 | SD32 | semidirect |
| 62. C3×Q16 | C2×C3⋊D3 | semidirect |
| 73. C2×Q16 | C3⋊(C3⋊D3) | semidirect |
| 77. C33 | C2×SD32 | semidirect |
| 87. C2×C32 | #828 | semidirect |
| 93. Q16 | C2×C3⋊(C3⋊D3) | semidirect |
| 104. C32 | C2×#828 | semidirect |
| 114. C2×C3 | #63655 | semidirect |
| 123. C3 | C2×#63655 | semidirect |
| 125. C2 | #11722198 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×Q16 | 2 |
| C2×#88852 | 2 |
| #11722198 | 2 |
| C2×C3⋊(C3⋊(C3⋊C16)) | 2 |
| C2×#63655 | 3 |