Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
353 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 353 conjugacy classes of subgroups — too many to draw. Only its 91 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×C9×SL(2,𝔽3) | C3 | semidirect |
| 4. #10619584 | C3 | semidirect |
| 5. (C3×SL(2,𝔽3))⋊C9 | C3 | semidirect |
| 14. Q8⋊H(3,𝔽3) | C9 | direct (N × H) |
| 28. C32×C9 | SL(2,𝔽3) | semidirect |
| 33. C32×Q8 | C3×C9 | semidirect |
| 37. C3×SL(2,𝔽3) | C3×C9 | semidirect |
| 39. Q8×C9 | H(3,𝔽3) | semidirect |
| 87. C32 | C9×SL(2,𝔽3) | semidirect |
| 91. C9 | Q8⋊H(3,𝔽3) | direct (N × H) |
| 92. Q8 | C9×H(3,𝔽3) | semidirect |
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×C9×SL(2,𝔽3) | 3 |
| #10619584 | 3 |
| (C3×SL(2,𝔽3))⋊C9 | 3 |
| C2×C9×H(3,𝔽3) | 4 |