Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
614 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 614 conjugacy classes of subgroups — too many to draw. Only its 93 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. C3×#63459 | C2 | semidirect |
| 3. C2×#88423 | C2 | semidirect |
| 4. C2×#88416 | C2 | semidirect |
| 5. #11720528 | C2 | semidirect |
| 6. C9×#809 | C2 | semidirect |
| 7. (C2×D9)⋊(C3⋊C8) | C2 | semidirect |
| 14. C2×C3×Dic18 | C22 | semidirect |
| 18. C3×C9×C4⋊C4 | C22 | semidirect |
| 19. C2×C3⋊(C9⋊C8) | C22 | semidirect |
| 22. C2×C9×C3⋊C8 | C22 | semidirect |
| 35. #63459 | D3 | semidirect |
| 86. C2×Dic18 | C2×D3 | semidirect |
| 89. C9×C4⋊C4 | C2×D3 | semidirect |
| 105. C2×C3×D9 | SD16 | semidirect |
| 126. #809 | D9 | semidirect |
| 202. C3×C4⋊C4 | C2×D9 | semidirect |
| 213. C2×C3⋊C8 | C2×D9 | semidirect |
| 245. C2×D9 | #215 | semidirect |
| 261. C3×C9 | #450 | semidirect |
| 339. C4⋊C4 | D3×D9 | semidirect |
| 382. C9 | #5046 | semidirect |
| 437. C3 | #10588456 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D9×D12 | 2 |
| C3×#63459 | 2 |
| C2×#88423 | 2 |
| C2×#88416 | 2 |
| #11720528 | 2 |
| C9×#809 | 2 |
| (C2×D9)⋊(C3⋊C8) | 2 |
| #10590596 | 3 |
| #10588456 | 3 |