Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
952 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 952 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×D8 | C2 | semidirect |
| 2. C3×#64141 | C2 | semidirect |
| 3. C3×#64110 | C2 | semidirect |
| 4. C3×#63660 | C2 | semidirect |
| 5. C3×#63646 | C2 | semidirect |
| 6. #10592859 | C3 | direct (N × H) |
| 20. C2×C32×D8 | D3 | semidirect |
| 21. C2×C32×D8 | C2×C3 | semidirect |
| 22. #64141 | C2×C3 | semidirect |
| 23. #64110 | C2×C3 | semidirect |
| 26. #63660 | C2×C3 | semidirect |
| 27. #63646 | C2×C3 | semidirect |
| 79. C2×C3×D8 | C3×D3 | semidirect |
| 80. C2×C3×D8 | C3⋊D3 | semidirect |
| 169. C2×D8 | C3×C3⋊D3 | semidirect |
| 173. C33 | #472 | semidirect |
| 246. C32 | #5160 | semidirect |
| 247. C32 | C3×#472 | semidirect |
| 279. C3 | C3×#5160 | semidirect |
| 280. C3 | #10592859 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×D8 | 2 |
| C3×#64141 | 2 |
| C3×#64110 | 2 |
| C3×#63660 | 2 |
| C3×#63646 | 2 |
| #10592859 | 3 |
| C3×#5160 | 3 |