Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1696 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 1696 conjugacy classes of subgroups — too many to draw. Only its 161 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×(C3⋊Dic3)⋊A4 | C2 | direct (N × H) |
| 3. C24×C3⋊Dic3 | C3 | semidirect |
| 5. C22×C22⋊H(3,𝔽3) | C4 | semidirect |
| 8. (C3⋊Dic3)⋊A4 | C22 | direct (N × H) |
| 15. C23×C3⋊Dic3 | C2×C3 | semidirect |
| 18. C2×C22⋊H(3,𝔽3) | C2×C4 | semidirect |
| 27. C24×C32 | C3×C4 | semidirect |
| 31. C22×C3×A4 | Dic3 | semidirect |
| 40. C22×C3⋊Dic3 | A4 | semidirect |
| 41. C22×C3⋊Dic3 | C22×C3 | semidirect |
| 46. C22⋊H(3,𝔽3) | C22×C4 | semidirect |
| 72. C23×C32 | C2×C3×C4 | semidirect |
| 77. C2×C3×A4 | C2×Dic3 | semidirect |
| 84. C2×C3⋊Dic3 | C2×A4 | semidirect |
| 136. C22×C32 | C4×A4 | semidirect |
| 137. C22×C32 | C22×C3×C4 | semidirect |
| 140. C3×A4 | C22×Dic3 | semidirect |
| 142. C3⋊Dic3 | C22×A4 | semidirect |
| 200. C2×C32 | C2×C4×A4 | semidirect |
| 205. C24 | (C3⋊Dic3)⋊C3 | semidirect |
| 253. C32 | C22×C4×A4 | semidirect |
| 263. C23 | C2×(C3⋊Dic3)⋊C3 | semidirect |
| 295. C22 | (C3⋊Dic3)⋊A4 | direct (N × H) |
| 296. C22 | C22×(C3⋊Dic3)⋊C3 | semidirect |
| 307. C2 | C2×(C3⋊Dic3)⋊A4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C22⋊H(3,𝔽3) | 2 |
| C2×(C3⋊Dic3)⋊A4 | 2 |
| C24×C3⋊Dic3 | 3 |
| C22×Dic3×A4 | 3 |
| C22×(C3⋊Dic3)⋊C3 | 4 |