Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
537 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 537 conjugacy classes of subgroups — too many to draw. Only its 116 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×#737 | C2 | semidirect |
| 2. S4×3−1+2 | C3 | semidirect |
| 4. C3×C9×S4 | C3 | semidirect |
| 8. C22×#737 | D3 | semidirect |
| 10. A4×3−1+2 | C2×C3 | semidirect |
| 14. C3×C9×A4 | C2×C3 | semidirect |
| 30. C22×3−1+2 | C3×D3 | semidirect |
| 34. C22×C3×C9 | C3×D3 | semidirect |
| 49. #737 | S4 | direct (N × H) |
| 85. 3−1+2 | C3×S4 | semidirect |
| 93. C3×C9 | C3×S4 | semidirect |
| 94. S4 | #737 | direct (N × H) |
| 111. A4 | C2×#737 | semidirect |
| 130. C22 | D3×#737 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| A4×#737 | 2 |
| S4×3−1+2 | 3 |
| S4×H(3,𝔽3) | 3 |
| C3×C9×S4 | 3 |
| D4×#737 | 3 |
| D3×#737 | 4 |