Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
768 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 768 conjugacy classes of subgroups — too many to draw. Only its 144 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. C3×#64110 | C2 | semidirect |
| 2. C2×C32×D24 | C2 | semidirect |
| 3. #11723364 | C2 | semidirect |
| 4. #11722189 | C2 | semidirect |
| 5. #11722025 | C2 | semidirect |
| 21. #64110 | D3 | semidirect |
| 22. C2×C3×D24 | D3 | semidirect |
| 79. C2×D24 | C3⋊D3 | semidirect |
| 165. C33 | #472 | semidirect |
| 233. C32 | #5142 | semidirect |
| 234. C32 | #5160 | semidirect |
| 265. C3 | #10590926 | semidirect |
| 266. C3 | #10592859 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64110 | 2 |
| C2×C32×D24 | 2 |
| #11723364 | 2 |
| #11722189 | 2 |
| #11722025 | 2 |
| #10592859 | 3 |
| #10590926 | 3 |