Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
458 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 458 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. C4×C9×D12 | C2 | semidirect |
| 2. C3×#63436 | C2 | semidirect |
| 3. C2×#88421 | C2 | semidirect |
| 4. C4⋊(C3⋊(C9⋊C8)) | C2 | semidirect |
| 5. #11720266 | C2 | semidirect |
| 25. #63436 | D3 | semidirect |
| 36. C9×D12 | D4 | semidirect |
| 75. C3×C4×C9 | D8 | semidirect |
| 84. C4×D12 | D9 | semidirect |
| 176. C4×C9 | #213 | semidirect |
| 184. C3×C9 | #459 | semidirect |
| 212. D12 | D36 | semidirect |
| 262. C3×C4 | #3673 | semidirect |
| 271. C9 | #5072 | semidirect |
| 308. C4 | #88421 | semidirect |
| 312. C3 | #10588698 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C9×D12 | 2 |
| C3×#63436 | 2 |
| C2×#88421 | 2 |
| C4⋊(C3⋊(C9⋊C8)) | 2 |
| #11720266 | 2 |
| #10590347 | 3 |
| #10588698 | 3 |