Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
3612 conjugacy classes of subgroups; only the 683 normal subgroups are shown.
This group has 3612 conjugacy classes of subgroups — too many to draw. Only its 683 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. C2×C33×Q16 | C2 | semidirect |
| 3. C2×#88863 | C2 | semidirect |
| 4. Q16×C3⋊(C3⋊D3) | C2 | direct (N × H) |
| 5. C2×#88853 | C2 | semidirect |
| 15. C33×Q16 | C22 | semidirect |
| 17. #88863 | C22 | semidirect |
| 19. #88853 | C22 | semidirect |
| 22. C2×C32×Q16 | D3 | semidirect |
| 50. C32×Q16 | C2×D3 | semidirect |
| 57. C2×C3⋊(C3⋊D3) | Q16 | direct (N × H) |
| 65. C2×C3×Q16 | C3⋊D3 | semidirect |
| 86. C2×C33 | C2×Q16 | semidirect |
| 88. C3⋊(C3⋊D3) | C2×Q16 | direct (N × H) |
| 96. C3×Q16 | C2×C3⋊D3 | semidirect |
| 114. C2×Q16 | C3⋊(C3⋊D3) | direct (N × H) |
| 116. C33 | C22×Q16 | semidirect |
| 132. C2×C32 | D3×Q16 | semidirect |
| 144. Q16 | C2×C3⋊(C3⋊D3) | direct (N × H) |
| 156. C32 | C2×D3×Q16 | semidirect |
| 172. C2×C3 | Q16×C3⋊D3 | semidirect |
| 183. C3 | C2×Q16×C3⋊D3 | semidirect |
| 185. C2 | Q16×C3⋊(C3⋊D3) | direct (N × H) |
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×C33×Q16 | 2 |
| C2×#88863 | 2 |
| Q16×C3⋊(C3⋊D3) | 2 |
| C2×#88853 | 2 |
| C2×C8×C3⋊(C3⋊D3) | 2 |
| C2×Q16×C3⋊D3 | 3 |