Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
336 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 40 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. #11757458 | C2 | direct (N × H) |
| 2. C23×C3×3−1+2 | C3 | semidirect |
| 4. C2×C3×#1094 | C3 | semidirect |
| 5. C2×C32⋊(C22⋊C9) | C3 | semidirect |
| 9. C22×C3×3−1+2 | C2×C3 | semidirect |
| 11. C3×#1094 | C2×C3 | semidirect |
| 12. C32⋊(C22⋊C9) | C2×C3 | semidirect |
| 25. C2×C3×3−1+2 | A4 | semidirect |
| 43. C3×3−1+2 | C2×A4 | semidirect |
| 162. C23 | #6857 | semidirect |
| 181. C22 | C2×#6857 | semidirect |
| 190. C2 | #11757458 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11757458 | 2 |
| C23×C3×3−1+2 | 3 |
| C2×C3×C22⋊H(3,𝔽3) | 3 |
| C2×C3×#1094 | 3 |
| C2×C32⋊(C22⋊C9) | 3 |
| C2×#6857 | 4 |