Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1932 conjugacy classes of subgroups; only the 489 normal subgroups are shown.
This group has 1932 conjugacy classes of subgroups — too many to draw. Only its 489 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 |
|---|---|---|
| 3. C33×C4⋊C8 | C2 | semidirect |
| 4. #11722184 | C2 | semidirect |
| 5. C4⋊(C3⋊(C3⋊(C3⋊C8))) | C2 | semidirect |
| 19. C32×C4⋊C8 | D3 | semidirect |
| 30. C4×C3⋊(C3⋊D3) | C8 | semidirect |
| 51. C33×C4 | C2×C8 | semidirect |
| 56. C3⋊(C3⋊Dic3) | C2×C8 | semidirect |
| 59. C3×C4⋊C8 | C3⋊D3 | semidirect |
| 79. C3⋊(C3⋊D3) | C4⋊C8 | direct (N × H) |
| 95. C32×C4 | D3×C8 | semidirect |
| 105. C4⋊C8 | C3⋊(C3⋊D3) | direct (N × H) |
| 106. C33 | C2×C4⋊C8 | semidirect |
| 139. C3×C4 | C8×C3⋊D3 | semidirect |
| 145. C32 | D3×C4⋊C8 | semidirect |
| 171. C4 | C8×C3⋊(C3⋊D3) | semidirect |
| 174. C3 | C3⋊D3×C4⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×C3⋊(C3⋊D3) | 2 |
| C42×C3⋊(C3⋊D3) | 2 |
| C33×C4⋊C8 | 2 |
| #11722184 | 2 |
| C4⋊(C3⋊(C3⋊(C3⋊C8))) | 2 |
| C3⋊D3×C4⋊C8 | 3 |