Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
451 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 451 conjugacy classes of subgroups — too many to draw. Only its 130 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 |
|---|---|---|
| 2. C3×#5093 | C2 | semidirect |
| 4. C3×#4680 | C2 | semidirect |
| 5. C3×C8×C3⋊C8 | C2 | semidirect |
| 7. #71256 | C3 | direct (N × H) |
| 23. #5093 | C2×C3 | semidirect |
| 25. #4680 | C2×C3 | semidirect |
| 27. C8×C3⋊C8 | C2×C3 | semidirect |
| 187. C32 | #1708 | semidirect |
| 216. C3 | #71256 | direct (N × H) |
| 217. C3 | C3×#1708 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#492 | 2 |
| C3×#5093 | 2 |
| C3×#5070 | 2 |
| C3×#4680 | 2 |
| C3×C8×C3⋊C8 | 2 |
| C3×#1708 | 3 |
| #71256 | 3 |