Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
160 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 62 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 |
|---|---|---|
| 5. #67584 | C3 | direct (N × H) |
| 117. C32 | #1420 | semidirect |
| 136. C3 | #67584 | direct (N × H) |
| 137. C3 | C3×#1420 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Dic24 | 2 |
| C32×#368 | 2 |
| C3×#4499 | 2 |
| C3×#1420 | 3 |
| #67584 | 3 |