Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
643 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 643 conjugacy classes of subgroups — too many to draw. Only its 147 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 |
|---|---|---|
| 4. C8×(C3⋊Dic3)⋊C3 | C2 | semidirect |
| 5. #11720310 | C2 | semidirect |
| 11. C8×#272 | C4 | semidirect |
| 15. #88434 | C4 | semidirect |
| 20. C8×C3⋊Dic3 | D3 | semidirect |
| 30. #6199 | C8 | direct (N × H) |
| 31. C8×H(3,𝔽3) | C2×C4 | semidirect |
| 32. #6180 | C2×C4 | semidirect |
| 33. (C3⋊(C3⋊C8))⋊C3 | C2×C4 | semidirect |
| 57. (C3⋊Dic3)⋊C3 | C2×C8 | semidirect |
| 85. C32×C8 | C4×D3 | semidirect |
| 86. C3⋊(C3⋊C8) | C4×D3 | semidirect |
| 93. #272 | C4×C8 | semidirect |
| 128. C3⋊Dic3 | D3×C8 | semidirect |
| 137. H(3,𝔽3) | C2×C4×C8 | semidirect |
| 204. C32 | C4×D3×C8 | semidirect |
| 214. C8 | #6199 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×#272 | 2 |
| C4×#6199 | 2 |
| C2×#88434 | 2 |
| C8×(C3⋊Dic3)⋊C3 | 2 |
| #11720310 | 2 |
| D3×C8×Dic3 | 3 |