Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
437 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 437 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 |
|---|---|---|
| 2. C32×#501 | C2 | semidirect |
| 4. C3×#5081 | C2 | semidirect |
| 5. C3×#4543 | C2 | semidirect |
| 6. C3×#4465 | C2 | semidirect |
| 9. #71391 | C3 | direct (N × H) |
| 33. C3×#501 | D3 | semidirect |
| 34. C3×#501 | C2×C3 | semidirect |
| 37. #5081 | C2×C3 | semidirect |
| 41. #4543 | C2×C3 | semidirect |
| 42. #4465 | C2×C3 | semidirect |
| 138. #501 | C3×D3 | semidirect |
| 355. C32 | #1660 | semidirect |
| 400. C3 | #71391 | direct (N × H) |
| 401. C3 | C3×#1660 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5699 | 2 |
| C32×#501 | 2 |
| C3×#5086 | 2 |
| C3×#5081 | 2 |
| C3×#4543 | 2 |
| C3×#4465 | 2 |
| C3×#4464 | 2 |
| C3×#1660 | 3 |
| #71391 | 3 |