Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
193 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 193 conjugacy classes of subgroups — too many to draw. Only its 82 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×#4499 | C2 | semidirect |
| 4. #67809 | C3 | direct (N × H) |
| 14. #4499 | C2×C3 | semidirect |
| 131. C32 | #1400 | semidirect |
| 156. C3 | #67809 | direct (N × H) |
| 157. C3 | C3×#1400 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×M32 | 2 |
| C3×#4499 | 2 |
| C3×#1400 | 3 |
| #67809 | 3 |