Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1680 conjugacy classes of subgroups; only the 413 normal subgroups are shown.
This group has 1680 conjugacy classes of subgroups — too many to draw. Only its 413 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. Q8×C3⋊(C3⋊Dic3) | C2 | semidirect |
| 4. C33×#103 | C2 | semidirect |
| 6. #11722185 | C2 | semidirect |
| 7. #11722177 | C2 | semidirect |
| 14. #88862 | C4 | semidirect |
| 24. C32×#103 | D3 | semidirect |
| 30. C33×Q8 | C2×C4 | semidirect |
| 41. C3⋊(C3⋊(C3⋊C8)) | C2×C4 | semidirect |
| 69. C3×#103 | C3⋊D3 | semidirect |
| 75. C32×Q8 | C4×D3 | semidirect |
| 119. #103 | C3⋊(C3⋊D3) | semidirect |
| 122. C33 | #440 | semidirect |
| 125. C3×Q8 | C4×C3⋊D3 | semidirect |
| 164. C32 | #4817 | semidirect |
| 167. Q8 | C4×C3⋊(C3⋊D3) | semidirect |
| 194. C3 | #10592516 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C3⋊(C3⋊Dic3) | 2 |
| C2×#88862 | 2 |
| #11723934 | 2 |
| C33×#103 | 2 |
| #11722191 | 2 |
| #11722185 | 2 |
| #11722177 | 2 |
| #10592516 | 3 |