Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
670 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 670 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 |
|---|---|---|
| 1. C2×D3×D4×C9 | C2 | semidirect |
| 2. C2×#88544 | C2 | semidirect |
| 3. #11721038 | C2 | semidirect |
| 4. C2×#88422 | C2 | semidirect |
| 5. C3×#63392 | C2 | semidirect |
| 6. #11720294 | C2 | semidirect |
| 7. (C2×D3)⋊(C9⋊C8) | C2 | semidirect |
| 12. C2×C4⋊(C3⋊D9) | C22 | semidirect |
| 20. C2×C3⋊(C9⋊C8) | C22 | semidirect |
| 21. C3×C4⋊Dic9 | C22 | semidirect |
| 22. C2×C3×C9⋊C8 | C22 | semidirect |
| 38. #63392 | D3 | semidirect |
| 48. C3×D4×C9 | D4 | semidirect |
| 56. C9×D12 | D4 | semidirect |
| 94. C4⋊Dic9 | C2×D3 | semidirect |
| 97. C2×C9⋊C8 | C2×D3 | semidirect |
| 111. C2×D3×C9 | D8 | semidirect |
| 117. C2×D3×D4 | D9 | semidirect |
| 168. D4×C9 | D12 | semidirect |
| 277. C3×C9 | #447 | semidirect |
| 301. C3×D4 | #611 | semidirect |
| 322. D12 | #611 | semidirect |
| 398. C2×D3 | #3673 | semidirect |
| 411. C9 | #4773 | semidirect |
| 426. D4 | #6195 | semidirect |
| 472. C3 | #10588898 | 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×#88544 | 2 |
| #11721038 | 2 |
| C2×#88422 | 2 |
| C3×#63392 | 2 |
| #11720294 | 2 |
| (C2×D3)⋊(C9⋊C8) | 2 |
| #10591448 | 3 |
| #10588898 | 3 |