Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
493 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 493 conjugacy classes of subgroups — too many to draw. Only its 127 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. C4×Q8×Dic3 | C3 | semidirect |
| 7. C3×C4×SL(2,𝔽3) | C4 | semidirect |
| 8. Dic3×SL(2,𝔽3) | C4 | direct (N × H) |
| 27. C3×C4×Q8 | C3×C4 | semidirect |
| 32. Q8×Dic3 | C3×C4 | semidirect |
| 40. C4×SL(2,𝔽3) | Dic3 | direct (N × H) |
| 49. C3×SL(2,𝔽3) | C42 | semidirect |
| 82. C4×Dic3 | SL(2,𝔽3) | direct (N × H) |
| 94. C4×Q8 | C3×Dic3 | semidirect |
| 109. C3×Q8 | C3×C42 | semidirect |
| 135. SL(2,𝔽3) | C4×Dic3 | direct (N × H) |
| 183. C3×C4 | C4×SL(2,𝔽3) | semidirect |
| 185. Dic3 | C4×SL(2,𝔽3) | direct (N × H) |
| 191. Q8 | C3×C4×Dic3 | semidirect |
| 233. C4 | Dic3×SL(2,𝔽3) | direct (N × H) |
| 236. C3 | C42×SL(2,𝔽3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×SL(2,𝔽3) | 2 |
| C2×Dic3×SL(2,𝔽3) | 2 |
| C4×Q8×Dic3 | 3 |
| C42×SL(2,𝔽3) | 3 |
| C2×C3×C4×Dic3 | 4 |