Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
307 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 307 conjugacy classes of subgroups — too many to draw. Only its 110 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 |
|---|---|---|
| 7. #68553 | C3 | direct (N × H) |
| 197. C32 | #1696 | semidirect |
| 228. C3 | #68553 | direct (N × H) |
| 229. C3 | C3×#1696 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4850 | 2 |
| C3×#4682 | 2 |
| C3×#4679 | 2 |
| C32×#334 | 2 |
| C3×#4481 | 2 |
| C3×#1696 | 3 |
| #68553 | 3 |