Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
614 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 614 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×C3×#3672 | C2 | semidirect |
| 3. #11720960 | C2 | semidirect |
| 4. C2×#88423 | C2 | semidirect |
| 5. #11720576 | C2 | semidirect |
| 6. #11720295 | C2 | semidirect |
| 7. (C2×D3)⋊(C9⋊C8) | C2 | semidirect |
| 17. C2×C3×Dic18 | C22 | semidirect |
| 18. C4⋊(C3⋊Dic9) | C22 | semidirect |
| 19. C2×C3⋊(C9⋊C8) | C22 | semidirect |
| 21. C2×C3×C9⋊C8 | C22 | semidirect |
| 34. C2×#3672 | D3 | semidirect |
| 86. C2×Dic18 | C2×D3 | semidirect |
| 95. C2×C9⋊C8 | C2×D3 | semidirect |
| 106. C2×D3×C9 | SD16 | semidirect |
| 261. C3×C9 | #450 | semidirect |
| 366. C2×D3 | #3672 | semidirect |
| 382. C9 | #5169 | semidirect |
| 437. 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×C3×#3672 | 2 |
| #11720960 | 2 |
| C2×#88423 | 2 |
| #11720576 | 2 |
| #11720295 | 2 |
| (C2×D3)⋊(C9⋊C8) | 2 |
| #10591458 | 3 |
| #10588897 | 3 |