Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
590 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 590 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. C34×Q8 | C3 | semidirect |
| 2. C3×Q8⋊H(3,𝔽3) | C3 | semidirect |
| 3. C3×#6204 | C3 | semidirect |
| 4. #10619585 | C3 | direct (N × H) |
| 12. C33×Q8 | C32 | semidirect |
| 15. Q8⋊H(3,𝔽3) | C32 | semidirect |
| 17. #6204 | C32 | semidirect |
| 28. C34 | SL(2,𝔽3) | semidirect |
| 67. C33 | C3×SL(2,𝔽3) | semidirect |
| 76. C3×Q8 | AΣL(1,𝔽27) | semidirect |
| 106. Q8 | C3×AΣL(1,𝔽27) | semidirect |
| 118. C3 | #10619585 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C34×Q8 | 3 |
| C3×Q8⋊H(3,𝔽3) | 3 |
| C3×#6204 | 3 |
| #10619585 | 3 |
| C2×C3×AΣL(1,𝔽27) | 4 |