Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
458 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 105 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. C9×#874 | C2 | semidirect |
| 2. C3×C4×D36 | C2 | semidirect |
| 3. C2×#88421 | C2 | semidirect |
| 4. C4⋊(C3⋊(C9⋊C8)) | C2 | semidirect |
| 5. #11720294 | C2 | semidirect |
| 25. C4×D36 | D3 | semidirect |
| 40. C3×D36 | D4 | semidirect |
| 75. C3×C4×C9 | D8 | semidirect |
| 83. #874 | D9 | semidirect |
| 118. D36 | D12 | semidirect |
| 175. C4×C9 | #213 | semidirect |
| 184. C3×C9 | #459 | semidirect |
| 262. C3×C4 | #3673 | semidirect |
| 271. C9 | #5015 | semidirect |
| 308. C4 | #88421 | semidirect |
| 312. C3 | #10588754 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#874 | 2 |
| C3×C4×D36 | 2 |
| C2×#88421 | 2 |
| C4⋊(C3⋊(C9⋊C8)) | 2 |
| #11720294 | 2 |
| #10590347 | 3 |
| #10588754 | 3 |