Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
4340 conjugacy classes of subgroups; only the 989 normal subgroups are shown.
This group has 4340 conjugacy classes of subgroups — too many to draw. Only its 989 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. C33×C4×Q8 | C2 | semidirect |
| 3. Q8×C3⋊(C3⋊Dic3) | C2 | semidirect |
| 4. #11723934 | C2 | semidirect |
| 5. #11723933 | C2 | semidirect |
| 6. C4×C4⋊(C3⋊(C3⋊D3)) | C2 | semidirect |
| 7. C42×C3⋊(C3⋊D3) | C2 | semidirect |
| 10. #89080 | C4 | direct (N × H) |
| 23. C32×C4×Q8 | D3 | semidirect |
| 30. C33×Q8 | C2×C4 | semidirect |
| 37. C4⋊(C3⋊(C3⋊D3)) | C2×C4 | semidirect |
| 40. C4×C3⋊(C3⋊D3) | C2×C4 | semidirect |
| 61. C33×C4 | #41 | semidirect |
| 64. C3⋊(C3⋊Dic3) | #41 | semidirect |
| 66. C3×C4×Q8 | C3⋊D3 | semidirect |
| 73. C32×Q8 | C4×D3 | semidirect |
| 108. C32×C4 | #239 | semidirect |
| 114. C4×Q8 | C3⋊(C3⋊D3) | semidirect |
| 119. C33 | C4×#41 | semidirect |
| 121. C3×Q8 | C4×C3⋊D3 | semidirect |
| 155. C3×C4 | #3832 | semidirect |
| 159. C32 | C4×#239 | semidirect |
| 161. Q8 | C4×C3⋊(C3⋊D3) | semidirect |
| 185. C4 | #89080 | direct (N × H) |
| 186. C3 | C4×#3832 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89080 | 2 |
| C33×C4×Q8 | 2 |
| Q8×C3⋊(C3⋊Dic3) | 2 |
| #11723934 | 2 |
| #11723933 | 2 |
| C4×C4⋊(C3⋊(C3⋊D3)) | 2 |
| C42×C3⋊(C3⋊D3) | 2 |
| C4×#3832 | 3 |