Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
632 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 107 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×#88543 | C2 | semidirect |
| 3. #11720961 | C2 | semidirect |
| 4. C2×#88424 | C2 | semidirect |
| 5. C3×#63392 | C2 | semidirect |
| 6. #11720294 | C2 | semidirect |
| 7. (C2×D3)⋊(C9⋊C8) | C2 | semidirect |
| 12. C2×#6226 | C22 | semidirect |
| 19. C2×C3⋊(C9⋊C8) | C22 | semidirect |
| 20. C3×C4⋊Dic9 | C22 | semidirect |
| 21. C2×C3×C9⋊C8 | C22 | semidirect |
| 38. #63392 | D3 | semidirect |
| 92. C4⋊Dic9 | C2×D3 | semidirect |
| 96. C2×C9⋊C8 | C2×D3 | semidirect |
| 107. C2×D3×C9 | SD16 | semidirect |
| 265. C3×C9 | #450 | semidirect |
| 372. C2×D3 | #3672 | semidirect |
| 388. C9 | #4776 | semidirect |
| 443. C3 | #10588897 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×D4×C9 | 2 |
| C2×#88543 | 2 |
| #11720961 | 2 |
| C2×#88424 | 2 |
| C3×#63392 | 2 |
| #11720294 | 2 |
| (C2×D3)⋊(C9⋊C8) | 2 |
| #10591459 | 3 |
| #10588897 | 3 |