Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
454 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 454 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×#6226 | C2 | semidirect |
| 3. C2×#88424 | C2 | semidirect |
| 4. C3×C4⋊(C9⋊C8) | C2 | semidirect |
| 5. #11720295 | C2 | semidirect |
| 28. C4⋊(C9⋊C8) | D3 | semidirect |
| 36. #6226 | D4 | semidirect |
| 74. C3×C4×C9 | SD16 | semidirect |
| 173. C4×C9 | #204 | semidirect |
| 185. C3×C9 | #460 | semidirect |
| 255. C3×C4 | #3672 | semidirect |
| 269. C9 | #4848 | semidirect |
| 301. C4 | #88424 | semidirect |
| 305. C3 | #10588752 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#6226 | 2 |
| C9×#874 | 2 |
| C2×#88424 | 2 |
| C3×C4⋊(C9⋊C8) | 2 |
| #11720295 | 2 |
| #10590377 | 3 |
| #10588752 | 3 |