Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
316 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 316 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. A4×#733 | C2 | direct (N × H) |
| 4. C23×#733 | C3 | semidirect |
| 5. C2×#66364 | C3 | semidirect |
| 6. C2×#66359 | C3 | semidirect |
| 12. C22×#733 | C2×C3 | semidirect |
| 13. #66364 | C2×C3 | semidirect |
| 14. #66359 | C2×C3 | semidirect |
| 31. C2×#733 | A4 | direct (N × H) |
| 49. #733 | C2×A4 | direct (N × H) |
| 97. C2×A4 | #733 | direct (N × H) |
| 119. A4 | C2×#733 | direct (N × H) |
| 128. C23 | C3×#733 | semidirect |
| 139. C22 | C2×C3×#733 | semidirect |
| 146. C2 | A4×#733 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| A4×#733 | 2 |
| C2×A4×3−1+2 | 3 |
| C2×C3×C9×A4 | 3 |
| C23×#733 | 3 |
| C2×#66364 | 3 |
| C2×#66359 | 3 |
| C2×C3×#733 | 4 |