Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
319 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 319 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 |
|---|---|---|
| 1. C32×#430 | C2 | semidirect |
| 3. C3×#4553 | C2 | semidirect |
| 4. C3×#4495 | C2 | semidirect |
| 5. C3×#4494 | C2 | semidirect |
| 7. #70723 | C3 | direct (N × H) |
| 19. C3×#430 | D3 | semidirect |
| 20. C3×#430 | C2×C3 | semidirect |
| 25. #4553 | C2×C3 | semidirect |
| 26. #4495 | C2×C3 | semidirect |
| 27. #4494 | C2×C3 | semidirect |
| 78. #430 | C3×D3 | semidirect |
| 211. C32 | #2238 | semidirect |
| 247. C3 | #70723 | direct (N × H) |
| 248. C3 | C3×#2238 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#430 | 2 |
| C3×#5135 | 2 |
| C3×#4553 | 2 |
| C3×#4495 | 2 |
| C3×#4494 | 2 |
| C3×#2238 | 3 |
| #70723 | 3 |