Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
556 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 106 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×#3754⋊C3 | C2 | semidirect |
| 3. C4×#634⋊C3 | C2 | semidirect |
| 4. #63659⋊C3 | C2 | semidirect |
| 5. C4⋊((C3⋊(C3⋊C8))⋊C3) | C2 | semidirect |
| 6. #10592774 | C3 | semidirect |
| 21. C2×#3754 | C2×C3 | semidirect |
| 22. C4×#634 | C2×C3 | semidirect |
| 25. #63659 | C2×C3 | semidirect |
| 26. C4⋊(C3⋊(C3⋊C8)) | C2×C3 | semidirect |
| 40. #634⋊C3 | D4 | semidirect |
| 74. C4×H(3,𝔽3) | SD16 | semidirect |
| 122. #634 | C3×D4 | semidirect |
| 186. C32×C4 | #214 | semidirect |
| 187. C32×C4 | C3×SD16 | semidirect |
| 201. H(3,𝔽3) | #460 | semidirect |
| 310. C32 | #5075 | semidirect |
| 311. C32 | C3×#460 | semidirect |
| 348. C4 | #3754⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| H(3,𝔽3)×#127 | 2 |
| C2×#3754⋊C3 | 2 |
| C4×#634⋊C3 | 2 |
| #63659⋊C3 | 2 |
| C4⋊((C3⋊(C3⋊C8))⋊C3) | 2 |
| #10592774 | 3 |
| C3×#5075 | 3 |