Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
225 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 225 conjugacy classes of subgroups — too many to draw. Only its 34 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 |
|---|---|---|
| 2. C4×#6857 | C2 | semidirect |
| 3. #11757284 | C2 | semidirect |
| 5. C4×#4181 | C3 | semidirect |
| 7. #92161 | C4 | direct (N × H) |
| 13. C4×C32⋊C9 | C2×C3 | semidirect |
| 14. #66328 | C2×C3 | semidirect |
| 15. #6857 | C2×C4 | semidirect |
| 24. #4181 | C3×C4 | semidirect |
| 41. C32⋊C9 | C2×C3×C4 | semidirect |
| 138. C4 | #92161 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#92161 | 2 |
| C4×#6857 | 2 |
| #11757284 | 2 |
| C3×C4×(C3⋊D3)⋊C3 | 3 |
| C4×#4181 | 3 |