Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
336 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 49 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. (C3⋊Dic3)⋊A4 | C2 | direct (N × H) |
| 3. C23×C3⋊Dic3 | C3 | semidirect |
| 5. C2×C22⋊H(3,𝔽3) | C4 | semidirect |
| 14. C22×C3⋊Dic3 | C2×C3 | semidirect |
| 17. C22⋊H(3,𝔽3) | C2×C4 | semidirect |
| 25. C23×C32 | C3×C4 | semidirect |
| 29. C2×C3×A4 | Dic3 | semidirect |
| 36. C2×C3⋊Dic3 | A4 | semidirect |
| 62. C22×C32 | C2×C3×C4 | semidirect |
| 65. C3×A4 | C2×Dic3 | semidirect |
| 67. C3⋊Dic3 | C2×A4 | semidirect |
| 105. C2×C32 | C4×A4 | semidirect |
| 141. C32 | C2×C4×A4 | semidirect |
| 145. C23 | (C3⋊Dic3)⋊C3 | semidirect |
| 174. C22 | C2×(C3⋊Dic3)⋊C3 | semidirect |
| 185. 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 |
|---|---|
| C22×C22⋊H(3,𝔽3) | 2 |
| (C3⋊Dic3)⋊A4 | 2 |
| C23×C3⋊Dic3 | 3 |
| C2×Dic3×A4 | 3 |
| C2×(C3⋊Dic3)⋊C3 | 4 |