Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
417 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 417 conjugacy classes of subgroups — too many to draw. Only its 138 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 |
|---|---|---|
| 3. C3×#4681 | C2 | semidirect |
| 4. C3×#4680 | C2 | semidirect |
| 5. C32×C82 | C2 | semidirect |
| 7. #68059 | C3 | direct (N × H) |
| 23. #4681 | C2×C3 | semidirect |
| 24. #4680 | C2×C3 | semidirect |
| 26. C3×C82 | D3 | semidirect |
| 27. C3×C82 | C2×C3 | semidirect |
| 75. C82 | C3×D3 | semidirect |
| 174. C32 | #1708 | semidirect |
| 202. C3 | #68059 | direct (N × H) |
| 203. C3 | C3×#1708 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4694 | 2 |
| C3×#4693 | 2 |
| C3×#4681 | 2 |
| C3×#4680 | 2 |
| C32×C82 | 2 |
| C3×#1708 | 3 |
| #68059 | 3 |