Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
724 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 724 conjugacy classes of subgroups — too many to draw. Only its 138 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. C2×C3×#4208 | C2 | semidirect |
| 2. C3×C4×#737 | C2 | semidirect |
| 3. C4⋊#4208 | C3 | direct (N × H) |
| 8. C2×#4208 | C2×C3 | semidirect |
| 12. C4×#737 | C2×C3 | semidirect |
| 15. C32×C4×C9 | D3 | semidirect |
| 16. C3×#737 | D4 | semidirect |
| 40. C3×C4×C9 | C3×D3 | semidirect |
| 43. #737 | C3×D4 | semidirect |
| 46. C32×C9 | D12 | semidirect |
| 81. C3×C9 | C3×D12 | semidirect |
| 101. C3×C4 | #4208 | semidirect |
| 118. C4 | C3×#4208 | semidirect |
| 121. C3 | C4⋊#4208 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#4208 | 2 |
| C3×C4×#737 | 2 |
| C4⋊#4208 | 3 |
| C3×C4⋊#272 | 3 |
| C3×C9×D12 | 3 |