Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
609 conjugacy classes of subgroups; only the 250 normal subgroups are shown.
This group has 609 conjugacy classes of subgroups — too many to draw. Only its 250 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. #69393 | C3 | direct (N × H) |
| 19. C32×C42 | C8 | semidirect |
| 61. C3×C42 | C3⋊C8 | semidirect |
| 62. C3×C42 | C3×C8 | semidirect |
| 109. C42 | C3×C3⋊C8 | semidirect |
| 128. C32 | #1839 | semidirect |
| 154. C3 | #69393 | direct (N × H) |
| 155. C3 | C3×#1839 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C43 | 2 |
| C3×#4524 | 2 |
| C3×#1839 | 3 |
| #69393 | 3 |