Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
514 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 103 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×C4⋊(C3⋊D9) | C2 | semidirect |
| 2. C9×#874 | C2 | semidirect |
| 3. C2×#88422 | C2 | semidirect |
| 4. C3×C4⋊(C9⋊C8) | C2 | semidirect |
| 5. #11720295 | C2 | semidirect |
| 28. C4⋊(C9⋊C8) | D3 | semidirect |
| 36. C4⋊(C3⋊D9) | D4 | semidirect |
| 78. C3×C4×C9 | D8 | semidirect |
| 85. #874 | D9 | semidirect |
| 188. C4×C9 | D24 | semidirect |
| 198. C3×C9 | #459 | semidirect |
| 283. C3×C4 | #3673 | semidirect |
| 294. C9 | #4843 | semidirect |
| 332. C4 | #88422 | semidirect |
| 336. C3 | #10588754 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C4⋊(C3⋊D9) | 2 |
| C9×#874 | 2 |
| C2×#88422 | 2 |
| C3×C4⋊(C9⋊C8) | 2 |
| #11720295 | 2 |
| #10590355 | 3 |
| #10588754 | 3 |