Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
644 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 644 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 |
|---|---|---|
| 1. C2×D9×D12 | C2 | semidirect |
| 2. C2×C9×D24 | C2 | semidirect |
| 3. #11721036 | C2 | semidirect |
| 4. C2×#88422 | C2 | semidirect |
| 5. #11720543 | C2 | semidirect |
| 6. C3×(C2×D9)⋊C8 | C2 | semidirect |
| 7. #11720295 | C2 | semidirect |
| 13. C2×C9×D12 | C22 | semidirect |
| 19. C2×C3×C8×C9 | C22 | semidirect |
| 20. C4⋊(C3⋊Dic9) | C22 | semidirect |
| 21. C2×C3×C9⋊C8 | C22 | semidirect |
| 39. (C2×D9)⋊C8 | D3 | semidirect |
| 50. C4⋊(C3⋊D9) | D4 | semidirect |
| 55. C9×D12 | D4 | semidirect |
| 91. C2×C8×C9 | C2×D3 | semidirect |
| 96. C2×C9⋊C8 | C2×D3 | semidirect |
| 109. C2×C3×D9 | D8 | semidirect |
| 122. C2×D24 | D9 | semidirect |
| 205. C2×D12 | C2×D9 | semidirect |
| 210. C2×C3×C8 | C2×D9 | semidirect |
| 256. C2×D9 | D24 | semidirect |
| 271. C3×C9 | #447 | semidirect |
| 314. D12 | #611 | semidirect |
| 352. C2×C8 | D3×D9 | semidirect |
| 400. C9 | #4732 | semidirect |
| 460. C3 | #10588836 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D9×D12 | 2 |
| C2×C9×D24 | 2 |
| #11721036 | 2 |
| C2×#88422 | 2 |
| #11720543 | 2 |
| C3×(C2×D9)⋊C8 | 2 |
| #11720295 | 2 |
| #10590944 | 3 |
| #10588836 | 3 |