Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
580 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 580 conjugacy classes of subgroups — too many to draw. Only its 158 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. C3×#557⋊C3 | C2 | semidirect |
| 4. C3×#3504 | C3 | semidirect |
| 5. #3504⋊C3 | C3 | direct (N × H) |
| 17. #557⋊C3 | C2×C3 | semidirect |
| 20. C3×#41⋊C3 | Q8 | semidirect |
| 25. #3504 | C32 | semidirect |
| 69. #41⋊C3 | C3×Q8 | semidirect |
| 203. C3 | #3504⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#557⋊C3 | 2 |
| C3×#520⋊C3 | 2 |
| C3×C4×#41⋊C3 | 2 |
| C3×#3504 | 3 |
| #3504⋊C3 | 3 |
| C32×#125 | 4 |