Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
165 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 165 conjugacy classes of subgroups — too many to draw. Only its 114 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 |
|---|---|---|
| 4. #67508 | C3 | direct (N × H) |
| 8. C3×C3⋊C32 | C4 | semidirect |
| 30. C3⋊C32 | C3×C4 | semidirect |
| 95. C32 | #1397 | semidirect |
| 112. C3 | #67508 | direct (N × H) |
| 113. C3 | C3×#1397 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C4×C16 | 2 |
| C2×C3×C3⋊C32 | 2 |
| C3×#1397 | 3 |
| #67508 | 3 |