Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
502 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 96 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×#4169 | C2 | semidirect |
| 2. C3×C4×C32⋊C9 | C2 | semidirect |
| 4. C3×C4⋊(C3⋊D9) | C3 | semidirect |
| 5. C4⋊#4169 | C3 | direct (N × H) |
| 10. C2×C3×C3⋊D9 | C2×C3 | semidirect |
| 12. C32×C4×C9 | C2×C3 | semidirect |
| 13. C2×#4169 | C2×C3 | semidirect |
| 15. C4×C32⋊C9 | C2×C3 | semidirect |
| 16. C3×C32⋊C9 | D4 | semidirect |
| 22. C4⋊(C3⋊D9) | C32 | semidirect |
| 43. C33×C4 | D9 | semidirect |
| 46. C2×C3⋊D9 | C2×C32 | semidirect |
| 54. C3×C4×C9 | C2×C32 | semidirect |
| 57. C32×C9 | C3×D4 | semidirect |
| 59. C32⋊C9 | C3×D4 | semidirect |
| 113. C32×C4 | C3×D9 | semidirect |
| 127. C33 | D36 | semidirect |
| 136. C3×C9 | C32×D4 | semidirect |
| 181. C3×C4 | #4169 | semidirect |
| 198. C32 | C3×D36 | semidirect |
| 221. C4 | C3×#4169 | semidirect |
| 227. C3 | C4⋊#4169 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#4169 | 2 |
| C3×C4×C32⋊C9 | 2 |
| C32×C4⋊(C3⋊D3) | 3 |
| C3×C4⋊(C3⋊D9) | 3 |
| C4⋊#4169 | 3 |