Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
275 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 275 conjugacy classes of subgroups — too many to draw. Only its 94 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. C3×#4680 | C2 | semidirect |
| 3. C32×#364 | C2 | semidirect |
| 5. C3×#4513 | C2 | semidirect |
| 7. #69307 | C3 | direct (N × H) |
| 20. #4680 | C2×C3 | semidirect |
| 23. C3×#364 | D3 | semidirect |
| 24. C3×#364 | C2×C3 | semidirect |
| 27. #4513 | C2×C3 | semidirect |
| 36. C3×Dic12 | Q8 | semidirect |
| 37. C3×D24 | Q8 | semidirect |
| 79. #364 | C3×D3 | semidirect |
| 105. Dic12 | C3×Q8 | semidirect |
| 106. D24 | C3×Q8 | semidirect |
| 196. C32 | #2230 | semidirect |
| 226. C3 | #69307 | direct (N × H) |
| 227. C3 | C3×#2230 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4700 | 2 |
| C3×#4680 | 2 |
| C32×#364 | 2 |
| C3×#4518 | 2 |
| C3×#4513 | 2 |
| C3×#2230 | 3 |
| #69307 | 3 |