Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1121 conjugacy classes of subgroups; only the 271 normal subgroups are shown.
This group has 1121 conjugacy classes of subgroups — too many to draw. Only its 271 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 |
|---|---|---|
| 2. C2×Dic3×SL(2,𝔽3) | C2 | direct (N × H) |
| 3. C22×Q8×Dic3 | C3 | semidirect |
| 6. C22×C3×SL(2,𝔽3) | C4 | semidirect |
| 8. Dic3×SL(2,𝔽3) | C22 | direct (N × H) |
| 13. C2×Q8×Dic3 | C2×C3 | semidirect |
| 20. C2×C3×SL(2,𝔽3) | C2×C4 | semidirect |
| 25. C22×C3×Q8 | C3×C4 | semidirect |
| 33. C22×SL(2,𝔽3) | Dic3 | direct (N × H) |
| 37. Q8×Dic3 | C22×C3 | semidirect |
| 49. C3×SL(2,𝔽3) | C22×C4 | semidirect |
| 63. C2×C3×Q8 | C2×C3×C4 | semidirect |
| 73. C22×Dic3 | SL(2,𝔽3) | direct (N × H) |
| 77. C2×SL(2,𝔽3) | C2×Dic3 | direct (N × H) |
| 91. C22×Q8 | C3×Dic3 | semidirect |
| 119. C3×Q8 | C22×C3×C4 | semidirect |
| 129. C2×Dic3 | C2×SL(2,𝔽3) | direct (N × H) |
| 132. SL(2,𝔽3) | C22×Dic3 | direct (N × H) |
| 143. C2×Q8 | C2×C3×Dic3 | semidirect |
| 167. C22×C3 | C4×SL(2,𝔽3) | semidirect |
| 177. Dic3 | C22×SL(2,𝔽3) | direct (N × H) |
| 187. Q8 | C22×C3×Dic3 | semidirect |
| 205. C2×C3 | C2×C4×SL(2,𝔽3) | semidirect |
| 209. C22 | Dic3×SL(2,𝔽3) | direct (N × H) |
| 221. C3 | C22×C4×SL(2,𝔽3) | semidirect |
| 222. C2 | C2×Dic3×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 |
|---|---|
| C23×C3×SL(2,𝔽3) | 2 |
| C2×Dic3×SL(2,𝔽3) | 2 |
| C22×Q8×Dic3 | 3 |
| C22×C4×SL(2,𝔽3) | 3 |
| C23×C3×Dic3 | 4 |