Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
542 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 101 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×#88523 | C2 | semidirect |
| 3. C2×(C3⋊D9)⋊C8 | C2 | semidirect |
| 4. C9×(C2×D3)⋊C8 | C2 | semidirect |
| 5. C3×(C2×D9)⋊C8 | C2 | semidirect |
| 6. (C2×D3)⋊(C9⋊C8) | C2 | semidirect |
| 7. (C2×D9)⋊(C3⋊C8) | C2 | semidirect |
| 39. (C2×D9)⋊C8 | D3 | semidirect |
| 126. (C2×D3)⋊C8 | D9 | semidirect |
| 261. C3×C9 | #408 | semidirect |
| 381. C9 | #4727 | semidirect |
| 435. C3 | #10588409 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88640 | 2 |
| C2×#88523 | 2 |
| C2×(C3⋊D9)⋊C8 | 2 |
| C9×(C2×D3)⋊C8 | 2 |
| C3×(C2×D9)⋊C8 | 2 |
| (C2×D3)⋊(C9⋊C8) | 2 |
| (C2×D9)⋊(C3⋊C8) | 2 |
| #10590959 | 3 |
| #10588409 | 3 |