Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
965 conjugacy classes of subgroups; only the 282 normal subgroups are shown.
This group has 965 conjugacy classes of subgroups — too many to draw. Only its 282 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×C43 | C2 | semidirect |
| 3. C3×#4933 | C2 | semidirect |
| 5. #73317 | C3 | direct (N × H) |
| 13. C3×C43 | D3 | semidirect |
| 14. C3×C43 | C2×C3 | semidirect |
| 16. #4933 | C2×C3 | semidirect |
| 41. C43 | C3×D3 | semidirect |
| 97. C32 | #2866 | semidirect |
| 114. C3 | #73317 | direct (N × H) |
| 115. C3 | C3×#2866 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C43 | 2 |
| C3×#4940 | 2 |
| C3×#4933 | 2 |
| C3×#2866 | 3 |
| #73317 | 3 |