Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1572 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 1572 conjugacy classes of subgroups — too many to draw. Only its 170 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×Q8×C3⋊(C3⋊D3) | C2 | semidirect |
| 2. C2×C32×#215 | C2 | semidirect |
| 4. C2×#88794 | C2 | semidirect |
| 5. C3×#63662 | C2 | semidirect |
| 6. #11722042 | C2 | semidirect |
| 7. #11722024 | C2 | semidirect |
| 31. C2×C3×#215 | D3 | semidirect |
| 34. #63662 | D3 | semidirect |
| 43. C33×Q8 | D4 | semidirect |
| 53. #6308 | D4 | semidirect |
| 102. C2×C3⋊(C3⋊D3) | SD16 | semidirect |
| 116. C2×#215 | C3⋊D3 | semidirect |
| 136. C32×Q8 | D12 | semidirect |
| 137. C32×Q8 | #67 | semidirect |
| 265. C33 | #448 | semidirect |
| 275. C3×Q8 | #626 | semidirect |
| 276. C3×Q8 | #638 | semidirect |
| 384. C32 | #4806 | semidirect |
| 385. C32 | #5170 | semidirect |
| 392. Q8 | #6291 | semidirect |
| 434. C3 | #10591592 | semidirect |
| 435. C3 | #10592869 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×C3⋊(C3⋊D3) | 2 |
| C2×C32×#215 | 2 |
| #11723531 | 2 |
| C2×#88794 | 2 |
| C3×#63662 | 2 |
| #11722042 | 2 |
| #11722024 | 2 |
| #10592869 | 3 |
| #10591592 | 3 |