Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
169 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 169 conjugacy classes of subgroups — too many to draw. Only its 98 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. #67501 | C3 | direct (N × H) |
| 19. C32×C16 | C8 | semidirect |
| 56. C3×C16 | C3⋊C8 | semidirect |
| 57. C3×C16 | C3×C8 | semidirect |
| 95. C16 | C3×C3⋊C8 | semidirect |
| 111. C32 | #1372 | semidirect |
| 134. C3 | #67501 | direct (N × H) |
| 135. C3 | C3×#1372 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C4×C16 | 2 |
| C3×#4458 | 2 |
| C3×#1372 | 3 |
| #67501 | 3 |