Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
888 conjugacy classes of subgroups; only the 270 normal subgroups are shown.
This group has 888 conjugacy classes of subgroups — too many to draw. Only its 270 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×SL(2,𝔽3) | C2 | direct (N × H) |
| 3. C2×C3×Q82 | C3 | semidirect |
| 4. C2×Q8×SL(2,𝔽3) | C3 | direct (N × H) |
| 9. C3×Q82 | C2×C3 | semidirect |
| 13. Q8×SL(2,𝔽3) | C2×C3 | direct (N × H) |
| 18. C2×C3×SL(2,𝔽3) | Q8 | direct (N × H) |
| 20. C2×Q82 | C32 | semidirect |
| 40. C3×SL(2,𝔽3) | C2×Q8 | direct (N × H) |
| 42. Q82 | C2×C32 | semidirect |
| 52. C2×C3×Q8 | SL(2,𝔽3) | direct (N × H) |
| 53. C2×C3×Q8 | C3×Q8 | semidirect |
| 60. C2×SL(2,𝔽3) | C3×Q8 | direct (N × H) |
| 91. C3×Q8 | C2×SL(2,𝔽3) | direct (N × H) |
| 92. C3×Q8 | C2×C3×Q8 | semidirect |
| 103. SL(2,𝔽3) | C2×C3×Q8 | direct (N × H) |
| 112. C2×Q8 | C3×SL(2,𝔽3) | direct (N × H) |
| 113. C2×Q8 | C32×Q8 | semidirect |
| 144. Q8 | C2×C3×SL(2,𝔽3) | direct (N × H) |
| 145. Q8 | C2×C32×Q8 | semidirect |
| 158. C2×C3 | Q8×SL(2,𝔽3) | direct (N × H) |
| 172. C3 | C2×Q8×SL(2,𝔽3) | direct (N × H) |
| 173. C2 | C3×Q8×SL(2,𝔽3) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Q8×SL(2,𝔽3) | 2 |
| C2×C3×C4×SL(2,𝔽3) | 2 |
| C2×C3×Q82 | 3 |
| C2×Q8×SL(2,𝔽3) | 3 |
| C22×C32×Q8 | 4 |