Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
513 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 513 conjugacy classes of subgroups — too many to draw. Only its 128 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. C4×C4⋊((C3⋊D3)⋊C3) | C2 | semidirect |
| 3. C4×C8×H(3,𝔽3) | C2 | semidirect |
| 4. #63648⋊C3 | C2 | semidirect |
| 5. #63645⋊C3 | C2 | semidirect |
| 6. C4×#3745 | C3 | semidirect |
| 15. #3745⋊C3 | C4 | direct (N × H) |
| 17. C4×C4⋊(C3⋊D3) | C2×C3 | semidirect |
| 21. C32×C4×C8 | D3 | semidirect |
| 22. C32×C4×C8 | C2×C3 | semidirect |
| 23. #63648 | C2×C3 | semidirect |
| 24. #63645 | C2×C3 | semidirect |
| 33. C4⋊((C3⋊D3)⋊C3) | C2×C4 | semidirect |
| 36. C8×H(3,𝔽3) | C2×C4 | semidirect |
| 55. #3745 | C3×C4 | semidirect |
| 64. C4×H(3,𝔽3) | D8 | semidirect |
| 97. C4⋊(C3⋊D3) | C2×C3×C4 | semidirect |
| 107. C32×C8 | C4×D3 | semidirect |
| 108. C32×C8 | C2×C3×C4 | semidirect |
| 156. C32×C4 | D24 | semidirect |
| 157. C32×C4 | C3×D8 | semidirect |
| 168. C4×C8 | (C3⋊D3)⋊C3 | semidirect |
| 169. H(3,𝔽3) | C4×D8 | semidirect |
| 257. C32 | C4×D24 | semidirect |
| 258. C32 | C3×C4×D8 | semidirect |
| 268. C8 | C4×(C3⋊D3)⋊C3 | semidirect |
| 290. C4 | #3745⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3745⋊C3 | 2 |
| C4×C4⋊((C3⋊D3)⋊C3) | 2 |
| C4×C8×H(3,𝔽3) | 2 |
| #63648⋊C3 | 2 |
| #63645⋊C3 | 2 |
| C4×#3745 | 3 |
| C3×C4×D24 | 3 |