Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
1352 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 1352 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
|---|---|---|
| 1. C3×#66368 | C2 | direct (N × H) |
| 2. C23×C34 | C3 | semidirect |
| 3. C2×C3×C22⋊H(3,𝔽3) | C3 | semidirect |
| 4. C2×C3×#1094 | C3 | semidirect |
| 5. C2×#66368 | C3 | direct (N × H) |
| 9. C22×C34 | C2×C3 | semidirect |
| 10. C3×C22⋊H(3,𝔽3) | C2×C3 | semidirect |
| 11. C3×#1094 | C2×C3 | semidirect |
| 12. #66368 | C2×C3 | direct (N × H) |
| 18. C23×C33 | C32 | semidirect |
| 21. C2×C22⋊H(3,𝔽3) | C32 | semidirect |
| 23. C2×#1094 | C32 | semidirect |
| 27. C2×C34 | A4 | semidirect |
| 45. C22×C33 | C2×C32 | semidirect |
| 48. C22⋊H(3,𝔽3) | C2×C32 | semidirect |
| 50. #1094 | C2×C32 | semidirect |
| 52. C34 | C2×A4 | semidirect |
| 82. C2×C33 | C3×A4 | semidirect |
| 120. C33 | C2×C3×A4 | semidirect |
| 129. C23×C3 | AΣL(1,𝔽27) | semidirect |
| 172. C22×C3 | C2×AΣL(1,𝔽27) | semidirect |
| 186. C23 | C3×AΣL(1,𝔽27) | semidirect |
| 201. C2×C3 | #66368 | direct (N × H) |
| 205. C22 | C2×C3×AΣL(1,𝔽27) | semidirect |
| 210. C3 | C2×#66368 | direct (N × H) |
| 214. C2 | C3×#66368 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#66368 | 2 |
| C23×C34 | 3 |
| C2×C3×C22⋊H(3,𝔽3) | 3 |
| C2×C3×#1094 | 3 |
| C2×#66368 | 3 |
| C2×C3×AΣL(1,𝔽27) | 4 |