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. #67500 | C3 | direct (N × H) |
| 19. C32×C16 | C8 | semidirect |
| 56. C3×C16 | C3⋊C8 | semidirect |
| 57. C3×C16 | C3×C8 | semidirect |
| 96. C16 | C3×C3⋊C8 | semidirect |
| 115. C32 | #1371 | semidirect |
| 139. C3 | #67500 | direct (N × H) |
| 140. C3 | C3×#1371 | 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×#1371 | 3 |
| #67500 | 3 |