Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
357 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 357 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×#4699 | C2 | semidirect |
| 4. C32×C4⋊C16 | C2 | semidirect |
| 5. C3×#4503 | C2 | semidirect |
| 7. #69287 | C3 | direct (N × H) |
| 22. #4699 | C2×C3 | semidirect |
| 25. C3×C4⋊C16 | D3 | semidirect |
| 26. C3×C4⋊C16 | C2×C3 | semidirect |
| 28. #4503 | C2×C3 | semidirect |
| 85. C4⋊C16 | C3×D3 | semidirect |
| 128. C32×C4 | SD32 | semidirect |
| 214. C3×C4 | #800 | semidirect |
| 215. C3×C4 | C3×SD32 | semidirect |
| 222. C32 | #2208 | semidirect |
| 255. C4 | C3×#800 | semidirect |
| 259. C3 | #69287 | direct (N × H) |
| 260. C3 | C3×#2208 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#800 | 2 |
| C3×#4699 | 2 |
| C3×C4×D24 | 2 |
| C32×C4⋊C16 | 2 |
| C3×#4503 | 2 |
| C3×#2208 | 3 |
| #69287 | 3 |