Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1792 conjugacy classes of subgroups; only the 407 normal subgroups are shown.
This group has 1792 conjugacy classes of subgroups — too many to draw. Only its 407 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×SD16 | C2 | semidirect |
| 2. Q8×C3⋊(C3⋊Dic3) | C2 | semidirect |
| 3. C2×#88862 | C2 | semidirect |
| 5. #11722202 | C2 | semidirect |
| 6. #11722191 | C2 | semidirect |
| 7. #11722184 | C2 | semidirect |
| 22. C2×C32×SD16 | D3 | semidirect |
| 32. C33×Q8 | D4 | semidirect |
| 72. C3⋊(C3⋊Dic3) | SD16 | semidirect |
| 73. C2×C3×SD16 | C3⋊D3 | semidirect |
| 83. C32×Q8 | #67 | semidirect |
| 130. C2×SD16 | C3⋊(C3⋊D3) | semidirect |
| 136. C33 | #460 | semidirect |
| 140. C3×Q8 | #638 | semidirect |
| 185. C32 | #5163 | semidirect |
| 189. Q8 | #6312 | semidirect |
| 221. C3 | #10592862 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×SD16 | 2 |
| Q8×C3⋊(C3⋊Dic3) | 2 |
| C2×#88862 | 2 |
| #11723981 | 2 |
| #11722202 | 2 |
| #11722191 | 2 |
| #11722184 | 2 |
| #10592862 | 3 |