Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
374 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 9. #68376 | C3 | direct (N × H) |
| 318. C32 | #1663 | semidirect |
| 354. C3 | #68376 | direct (N × H) |
| 355. C3 | C3×#1663 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C3⋊#564 | 2 |
| C3×#5064 | 2 |
| C3×#4703 | 2 |
| C3×#4702 | 2 |
| C32×#330 | 2 |
| C3×#4465 | 2 |
| C3×#1663 | 3 |
| #68376 | 3 |