Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
147 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 147 conjugacy classes of subgroups — too many to draw. Only its 90 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. #67519 | C3 | direct (N × H) |
| 8. C3×C3⋊C32 | C4 | semidirect |
| 30. C3⋊C32 | C3×C4 | semidirect |
| 95. C32 | #1398 | semidirect |
| 112. C3 | #67519 | direct (N × H) |
| 113. C3 | C3×#1398 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#346 | 2 |
| C3×#4499 | 2 |
| C3×#1398 | 3 |
| #67519 | 3 |