Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
309 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 309 conjugacy classes of subgroups — too many to draw. Only its 110 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×#4682 | C2 | semidirect |
| 3. C32×C4⋊C16 | C2 | semidirect |
| 5. C3×#4504 | C2 | semidirect |
| 7. #69289 | C3 | direct (N × H) |
| 20. #4682 | C2×C3 | semidirect |
| 23. C3×C4⋊C16 | D3 | semidirect |
| 24. C3×C4⋊C16 | C2×C3 | semidirect |
| 27. #4504 | C2×C3 | semidirect |
| 39. C3×D24 | Q8 | semidirect |
| 78. C4⋊C16 | C3×D3 | semidirect |
| 106. D24 | C3×Q8 | semidirect |
| 203. C32 | #2224 | semidirect |
| 239. C3 | #69289 | direct (N × H) |
| 240. C3 | C3×#2224 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×D24 | 2 |
| C3×#4682 | 2 |
| C32×C4⋊C16 | 2 |
| C3×#4509 | 2 |
| C3×#4504 | 2 |
| C3×#2224 | 3 |
| #69289 | 3 |