Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
308 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 308 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. C3×Q8×H(3,𝔽3) | C3 | semidirect |
| 2. C3×Q8⋊H(3,𝔽3) | C3 | semidirect |
| 3. C32×Q8⋊C9 | C3 | semidirect |
| 4. #10619579 | C3 | direct (N × H) |
| 12. Q8×H(3,𝔽3) | C32 | semidirect |
| 14. Q8⋊H(3,𝔽3) | C32 | semidirect |
| 17. C3×Q8⋊C9 | C32 | semidirect |
| 27. C3×H(3,𝔽3) | SL(2,𝔽3) | semidirect |
| 61. H(3,𝔽3) | C3×SL(2,𝔽3) | semidirect |
| 68. C3×Q8 | #732 | semidirect |
| 94. Q8 | C3×#732 | semidirect |
| 106. C3 | #10619579 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Q8×H(3,𝔽3) | 3 |
| C3×Q8⋊H(3,𝔽3) | 3 |
| C32×Q8⋊C9 | 3 |
| #10619579 | 3 |
| C2×C3×#732 | 4 |