Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
934 conjugacy classes of subgroups; only the 222 normal subgroups are shown.
This group has 934 conjugacy classes of subgroups — too many to draw. Only its 222 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. #64145⋊C3 | C2 | semidirect |
| 3. #64144⋊C3 | C2 | semidirect |
| 4. D4×(C3⋊Dic3)⋊C3 | C2 | semidirect |
| 5. C4×#634⋊C3 | C2 | semidirect |
| 6. #10596184 | C3 | semidirect |
| 21. #64145 | C2×C3 | semidirect |
| 22. #64144 | C2×C3 | semidirect |
| 23. D4×C3⋊Dic3 | C2×C3 | semidirect |
| 24. C4×#634 | C2×C3 | semidirect |
| 171. H(3,𝔽3) | #559 | semidirect |
| 250. C32 | #5713 | semidirect |
| 251. C32 | C3×#559 | 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 |
| #64145⋊C3 | 2 |
| #64144⋊C3 | 2 |
| D4×(C3⋊Dic3)⋊C3 | 2 |
| C4×#634⋊C3 | 2 |
| #10596184 | 3 |
| C3×#5713 | 3 |