Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
394 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 394 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 |
|---|---|---|
| 1. C3×C3⋊#564 | C2 | semidirect |
| 4. C32×#330 | C2 | semidirect |
| 5. C3×#4465 | C2 | semidirect |
| 7. #68375 | C3 | direct (N × H) |
| 20. C3⋊#564 | C2×C3 | semidirect |
| 27. C3×#330 | D3 | semidirect |
| 28. C3×#330 | C2×C3 | semidirect |
| 29. #4465 | C2×C3 | semidirect |
| 84. #330 | C3×D3 | semidirect |
| 200. C32 | #1658 | semidirect |
| 228. C3 | #68375 | direct (N × H) |
| 229. C3 | C3×#1658 | 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×#5067 | 2 |
| C3×#4713 | 2 |
| C32×#330 | 2 |
| C3×#4465 | 2 |
| C3×#1658 | 3 |
| #68375 | 3 |