Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
225 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 225 conjugacy classes of subgroups — too many to draw. Only its 44 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. #73015 | C3 | direct (N × H) |
| 38. C3×SL(2,𝔽3) | Q16 | semidirect |
| 78. C3×Q8 | Dic12 | semidirect |
| 89. SL(2,𝔽3) | C3×Q16 | semidirect |
| 127. Q8 | C3×Dic12 | semidirect |
| 153. C3 | #73015 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5386 | 2 |
| C3×C8×SL(2,𝔽3) | 2 |
| #73015 | 3 |
| C3×#1670 | 3 |
| C2×C3×Dic12 | 4 |