Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
328 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 82 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. #11757805 | C2 | direct (N × H) |
| 2. C2×A4×3−1+2 | C3 | semidirect |
| 4. C2×C3×C9⋊A4 | C3 | semidirect |
| 5. C23×#731 | C3 | semidirect |
| 6. C2×#66365 | C3 | semidirect |
| 7. C2×#66361 | C3 | semidirect |
| 8. C2×#66357 | C3 | semidirect |
| 10. A4×3−1+2 | C2×C3 | semidirect |
| 12. C3×C9⋊A4 | C2×C3 | semidirect |
| 15. C22×#731 | C2×C3 | semidirect |
| 16. #66365 | C2×C3 | semidirect |
| 17. #66361 | C2×C3 | semidirect |
| 18. #66357 | C2×C3 | semidirect |
| 22. C23×3−1+2 | C32 | semidirect |
| 24. C23×C3×C9 | C32 | semidirect |
| 27. C2×#1094 | C32 | semidirect |
| 28. C2×C3×C22⋊C9 | C32 | semidirect |
| 42. C2×#731 | A4 | semidirect |
| 47. C22×3−1+2 | C2×C32 | semidirect |
| 53. C22×C3×C9 | C2×C32 | semidirect |
| 56. #1094 | C2×C32 | semidirect |
| 57. C3×C22⋊C9 | C2×C32 | semidirect |
| 69. #731 | C2×A4 | semidirect |
| 90. C2×3−1+2 | C3×A4 | semidirect |
| 100. C2×C3×C9 | C3×A4 | semidirect |
| 127. 3−1+2 | C2×C3×A4 | semidirect |
| 133. C3×C9 | C2×C3×A4 | semidirect |
| 182. C23 | #6910 | semidirect |
| 197. C22 | C2×#6910 | semidirect |
| 206. C2 | #11757805 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11757805 | 2 |
| C2×A4×3−1+2 | 3 |
| C2×A4×H(3,𝔽3) | 3 |
| C2×C3×C9⋊A4 | 3 |
| C23×#731 | 3 |
| C2×#66365 | 3 |
| C2×#66361 | 3 |
| C2×#66357 | 3 |
| C2×#6910 | 4 |