Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
120 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 120 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. #67581 | C3 | direct (N × H) |
| 92. C32 | #1425 | semidirect |
| 108. C3 | #67581 | direct (N × H) |
| 109. C3 | C3×#1425 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#368 | 2 |
| C3×#4506 | 2 |
| C2×C3×C3⋊C32 | 2 |
| C3×#1425 | 3 |
| #67581 | 3 |