Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
504 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 2. C2×#88547 | C2 | semidirect |
| 4. C2×#88428 | C2 | semidirect |
| 5. C3×#63395 | C2 | semidirect |
| 6. #11720297 | C2 | semidirect |
| 38. #63395 | D3 | semidirect |
| 98. C2×D3×C9 | Q16 | semidirect |
| 240. C3×C9 | #451 | semidirect |
| 321. C2×D3 | #3674 | semidirect |
| 342. C9 | #4809 | semidirect |
| 385. C3 | #10588907 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×Q8×C9 | 2 |
| C2×#88547 | 2 |
| #11720961 | 2 |
| C2×#88428 | 2 |
| C3×#63395 | 2 |
| #11720297 | 2 |
| (C2×D3)⋊(C9⋊C8) | 2 |
| #10591595 | 3 |
| #10588907 | 3 |