Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
688 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 113 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. C22×C9×D12 | C2 | semidirect |
| 2. #11721819 | C2 | semidirect |
| 3. C2×#88422 | C2 | semidirect |
| 4. C3×#63389 | C2 | semidirect |
| 5. #11720295 | C2 | semidirect |
| 11. C2×C4⋊(C3⋊D9) | C22 | semidirect |
| 16. C4⋊(C3⋊Dic9) | C22 | semidirect |
| 17. C2×C3×C9⋊C8 | C22 | semidirect |
| 29. #63389 | D3 | semidirect |
| 44. C9×D12 | D4 | semidirect |
| 74. C2×C9⋊C8 | C2×D3 | semidirect |
| 77. C22×C3×C9 | D8 | semidirect |
| 90. C22×D12 | D9 | semidirect |
| 198. C22×C9 | D24 | semidirect |
| 217. C3×C9 | #447 | semidirect |
| 255. D12 | #611 | semidirect |
| 298. C22×C3 | #3673 | semidirect |
| 326. C9 | #4732 | semidirect |
| 369. C22 | #88422 | semidirect |
| 375. C3 | #10588898 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C9×D12 | 2 |
| #11721819 | 2 |
| C2×#88422 | 2 |
| C3×#63389 | 2 |
| #11720295 | 2 |
| #10591162 | 3 |
| #10588898 | 3 |