Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
260 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 70 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 |
|---|---|---|
| 3. C3×#3395 | C3 | semidirect |
| 4. #3395⋊C3 | C3 | direct (N × H) |
| 18. #3395 | C32 | semidirect |
| 35. C3×SL(2,𝔽3) | Q16 | semidirect |
| 84. SL(2,𝔽3) | C3×Q16 | semidirect |
| 143. C3 | #3395⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#557⋊C3 | 2 |
| C3×C8×SL(2,𝔽3) | 2 |
| C3×#3395 | 3 |
| #3395⋊C3 | 3 |
| C32×#107 | 4 |