Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
401 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 401 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 |
|---|---|---|
| 7. #71338 | C3 | direct (N × H) |
| 172. C32 | #1716 | semidirect |
| 196. C3 | #71338 | direct (N × H) |
| 197. C3 | C3×#1716 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#498 | 2 |
| C3×#5080 | 2 |
| C3×#5079 | 2 |
| C3×#4699 | 2 |
| C3×#4455 | 2 |
| C3×#1716 | 3 |
| #71338 | 3 |