Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
544 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 88 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. #11757837 | C2 | direct (N × H) |
| 2. C23×C3×H(3,𝔽3) | C3 | semidirect |
| 3. C2×C3×C22⋊H(3,𝔽3) | C3 | semidirect |
| 4. C2×C3×#1094 | C3 | semidirect |
| 5. C2×#66362 | C3 | semidirect |
| 9. C22×C3×H(3,𝔽3) | C2×C3 | semidirect |
| 10. C3×C22⋊H(3,𝔽3) | C2×C3 | semidirect |
| 11. C3×#1094 | C2×C3 | semidirect |
| 12. #66362 | C2×C3 | semidirect |
| 18. C23×H(3,𝔽3) | C32 | semidirect |
| 21. C2×C22⋊H(3,𝔽3) | C32 | semidirect |
| 24. C2×C3×C22⋊C9 | C32 | semidirect |
| 29. C2×C3×H(3,𝔽3) | A4 | semidirect |
| 43. C22×H(3,𝔽3) | C2×C32 | semidirect |
| 46. C22⋊H(3,𝔽3) | C2×C32 | semidirect |
| 49. C3×C22⋊C9 | C2×C32 | semidirect |
| 52. C3×H(3,𝔽3) | C2×A4 | semidirect |
| 80. C2×H(3,𝔽3) | C3×A4 | semidirect |
| 112. H(3,𝔽3) | C2×C3×A4 | semidirect |
| 166. C23 | #6911 | semidirect |
| 185. C22 | C2×#6911 | semidirect |
| 194. C2 | #11757837 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11757837 | 2 |
| C23×C3×H(3,𝔽3) | 3 |
| C2×C3×C22⋊H(3,𝔽3) | 3 |
| C2×C3×#1094 | 3 |
| C2×#66362 | 3 |
| C2×#6911 | 4 |