Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
745 conjugacy classes of subgroups; only the 410 normal subgroups are shown.
This group has 745 conjugacy classes of subgroups — too many to draw. Only its 410 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. #69434 | C3 | direct (N × H) |
| 10. C3×#803 | C4 | semidirect |
| 11. C3×C4×C3⋊C8 | C4 | semidirect |
| 39. #803 | C3×C4 | semidirect |
| 40. C4×C3⋊C8 | C3×C4 | semidirect |
| 123. C32 | #1726 | semidirect |
| 143. C3 | #69434 | direct (N × H) |
| 144. C3 | C3×#1726 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#376 | 2 |
| C2×C3×#803 | 2 |
| C2×C3×C4×C3⋊C8 | 2 |
| C3×#1726 | 3 |
| #69434 | 3 |