Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
266 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 64 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. C32×Q8×C9 | C3 | semidirect |
| 3. C3×#6204 | C3 | semidirect |
| 4. #10619574 | C3 | direct (N × H) |
| 12. C3×Q8×C9 | C32 | semidirect |
| 16. #6204 | C32 | semidirect |
| 28. C32×C9 | SL(2,𝔽3) | semidirect |
| 62. C3×C9 | C3×SL(2,𝔽3) | semidirect |
| 65. C3×Q8 | #731 | semidirect |
| 88. Q8 | C3×#731 | semidirect |
| 98. C3 | #10619574 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×Q8×C9 | 3 |
| C3×Q8⋊H(3,𝔽3) | 3 |
| C3×#6204 | 3 |
| #10619574 | 3 |
| C2×C3×#731 | 4 |