Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
450 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 151 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×C3×C9×Q16 | C2 | semidirect |
| 3. #11720567 | C2 | direct (N × H) |
| 4. C2×C3⋊(C9⋊C16) | C2 | semidirect |
| 10. C3×C9×Q16 | C22 | semidirect |
| 14. C3⋊(C9⋊C16) | C22 | semidirect |
| 19. C2×C9×Q16 | D3 | semidirect |
| 45. C9×Q16 | C2×D3 | semidirect |
| 56. C2×C3×Q16 | D9 | semidirect |
| 83. C2×C3×C9 | SD32 | semidirect |
| 92. C3×Q16 | C2×D9 | semidirect |
| 114. C2×Q16 | C3⋊D9 | semidirect |
| 118. C3×C9 | C2×SD32 | semidirect |
| 140. C2×C9 | #828 | semidirect |
| 146. Q16 | C2×C3⋊D9 | semidirect |
| 164. C9 | C2×#828 | semidirect |
| 174. C2×C3 | #63387 | semidirect |
| 186. C3 | C2×#63387 | semidirect |
| 189. C2 | #11720567 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C9×Q16 | 2 |
| C2×#88525 | 2 |
| #11720567 | 2 |
| C2×C3⋊(C9⋊C16) | 2 |
| C2×#63655 | 3 |
| C2×#63387 | 3 |