Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
369 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 369 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 |
|---|---|---|
| 7. #71316 | C3 | direct (N × H) |
| 132. C32×C4 | Q32 | semidirect |
| 215. C3×C4 | #829 | semidirect |
| 216. C3×C4 | C3×Q32 | semidirect |
| 223. C32 | #2209 | semidirect |
| 251. C4 | C3×#829 | semidirect |
| 255. C3 | #71316 | direct (N × H) |
| 256. C3 | C3×#2209 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#494 | 2 |
| C2×C3×#829 | 2 |
| C3×C4×Dic12 | 2 |
| C3×#4564 | 2 |
| C3×C4⋊(C3⋊C16) | 2 |
| C3×#2209 | 3 |
| #71316 | 3 |