Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
305 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 305 conjugacy classes of subgroups — too many to draw. Only its 106 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×#4683 | C2 | semidirect |
| 3. C32×C4×C16 | C2 | semidirect |
| 5. C3×#4503 | C2 | semidirect |
| 7. #69059 | C3 | direct (N × H) |
| 20. #4683 | C2×C3 | semidirect |
| 24. C3×C4×C16 | D3 | semidirect |
| 25. C3×C4×C16 | C2×C3 | semidirect |
| 27. #4503 | C2×C3 | semidirect |
| 76. C4×C16 | C3×D3 | semidirect |
| 183. C32 | #2242 | semidirect |
| 212. C3 | #69059 | direct (N × H) |
| 213. C3 | C3×#2242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4696 | 2 |
| C3×#4683 | 2 |
| C32×C4×C16 | 2 |
| C3×#4509 | 2 |
| C3×#4503 | 2 |
| C3×#2242 | 3 |
| #69059 | 3 |