Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
632 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 101 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. #11720945 | C2 | semidirect |
| 4. C2×#88415 | C2 | semidirect |
| 5. C9×#832 | C2 | semidirect |
| 6. (C2×D9)⋊(C3⋊C8) | C2 | semidirect |
| 7. #11720266 | C2 | semidirect |
| 12. C2×#6226 | C22 | semidirect |
| 19. C2×C3⋊(C9⋊C8) | C22 | semidirect |
| 20. C9×C4⋊Dic3 | C22 | semidirect |
| 21. C2×C9×C3⋊C8 | C22 | semidirect |
| 107. C2×C3×D9 | SD16 | semidirect |
| 124. #832 | D9 | semidirect |
| 212. C4⋊Dic3 | C2×D9 | semidirect |
| 217. C2×C3⋊C8 | C2×D9 | semidirect |
| 249. C2×D9 | #214 | semidirect |
| 265. C3×C9 | #450 | semidirect |
| 388. C9 | #5218 | semidirect |
| 443. C3 | #10588456 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D4×D9 | 2 |
| C2×#88543 | 2 |
| #11720945 | 2 |
| C2×#88415 | 2 |
| C9×#832 | 2 |
| (C2×D9)⋊(C3⋊C8) | 2 |
| #11720266 | 2 |
| #10591459 | 3 |
| #10588456 | 3 |