Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
727 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 727 conjugacy classes of subgroups — too many to draw. Only its 156 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×C4⋊((C3⋊Dic3)⋊C3) | C2 | semidirect |
| 3. H(3,𝔽3)×#95 | C2 | semidirect |
| 4. #10592376 | C3 | semidirect |
| 12. C2×C4⋊(C3⋊Dic3) | C2×C3 | semidirect |
| 16. C32×#95 | D3 | semidirect |
| 17. C32×#95 | C2×C3 | semidirect |
| 120. #95 | (C3⋊D3)⋊C3 | semidirect |
| 121. H(3,𝔽3) | #399 | semidirect |
| 194. C32 | #4677 | semidirect |
| 195. C32 | C3×#399 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3752⋊C3 | 2 |
| C2×C4⋊((C3⋊Dic3)⋊C3) | 2 |
| H(3,𝔽3)×#95 | 2 |
| #10592376 | 3 |
| C3×#4677 | 3 |