Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
563 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 563 conjugacy classes of subgroups — too many to draw. Only its 170 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 |
|---|---|---|
| 3. C3×#4543 | C2 | semidirect |
| 5. #71821 | C3 | direct (N × H) |
| 21. #4543 | C2×C3 | semidirect |
| 196. C32 | #1526 | semidirect |
| 225. C3 | #71821 | direct (N × H) |
| 226. C3 | C3×#1526 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#533 | 2 |
| C3×C4×#208 | 2 |
| C3×#4543 | 2 |
| C3×#1526 | 3 |
| #71821 | 3 |