Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
401 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 401 conjugacy classes of subgroups — too many to draw. Only its 57 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. C2×C3×#131⋊C3 | C2 | semidirect |
| 3. #5827⋊C3 | C2 | semidirect |
| 4. #83806 | C3 | semidirect |
| 8. #1010⋊C3 | C4 | semidirect |
| 15. C2×C3×#131 | C2×C3 | semidirect |
| 16. #5827 | C2×C3 | semidirect |
| 18. C2×#131⋊C3 | D3 | semidirect |
| 36. #1010 | C3×C4 | semidirect |
| 71. C2×#131 | C3×D3 | semidirect |
| 325. C3 | #2898⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1010⋊C3 | 2 |
| C2×C3×#131⋊C3 | 2 |
| #5827⋊C3 | 2 |
| #83806 | 3 |
| #2898⋊C3 | 3 |
| C3×#821 | 4 |