Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
729 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 729 conjugacy classes of subgroups — too many to draw. Only its 159 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. SL(2,𝔽3)×Dic6 | C2 | direct (N × H) |
| 4. C2×Q8×Dic6 | C3 | semidirect |
| 13. Q8×Dic6 | C2×C3 | semidirect |
| 25. C2×C3×SL(2,𝔽3) | Q8 | semidirect |
| 59. C3×SL(2,𝔽3) | C2×Q8 | semidirect |
| 71. C2×C3×Q8 | C3×Q8 | semidirect |
| 83. C2×Dic6 | SL(2,𝔽3) | direct (N × H) |
| 87. C2×SL(2,𝔽3) | Dic6 | direct (N × H) |
| 131. C3×Q8 | C2×C3×Q8 | semidirect |
| 151. Dic6 | C2×SL(2,𝔽3) | direct (N × H) |
| 153. SL(2,𝔽3) | C2×Dic6 | direct (N × H) |
| 164. C2×Q8 | C3×Dic6 | semidirect |
| 210. Q8 | C2×C3×Dic6 | semidirect |
| 231. C2×C3 | Q8×SL(2,𝔽3) | semidirect |
| 248. C3 | C2×Q8×SL(2,𝔽3) | semidirect |
| 249. C2 | SL(2,𝔽3)×Dic6 | direct (N × H) |
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 |
| SL(2,𝔽3)×Dic6 | 2 |
| C2×Q8×Dic6 | 3 |
| C2×Q8×SL(2,𝔽3) | 3 |
| C22×C3×Dic6 | 4 |