Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
840 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 170 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. C2×C33×Q16 | C2 | semidirect |
| 4. C3×#63663 | C2 | semidirect |
| 5. C3×#63646 | C2 | semidirect |
| 6. #10592891 | C3 | direct (N × H) |
| 20. C2×C32×Q16 | D3 | semidirect |
| 21. C2×C32×Q16 | C2×C3 | semidirect |
| 26. #63663 | C2×C3 | semidirect |
| 27. #63646 | C2×C3 | semidirect |
| 78. C2×C3×Q16 | C3×D3 | semidirect |
| 79. C2×C3×Q16 | C3⋊D3 | semidirect |
| 164. C2×Q16 | C3×C3⋊D3 | semidirect |
| 168. C33 | #473 | semidirect |
| 235. C32 | #5192 | semidirect |
| 236. C32 | C3×#473 | semidirect |
| 264. C3 | C3×#5192 | semidirect |
| 265. C3 | #10592891 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×Q16 | 2 |
| C3×#64151 | 2 |
| C3×#64110 | 2 |
| C3×#63663 | 2 |
| C3×#63646 | 2 |
| #10592891 | 3 |
| C3×#5192 | 3 |