Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
585 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 585 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 |
|---|---|---|
| 2. C32×#424 | C2 | semidirect |
| 3. C3×#5113 | C2 | semidirect |
| 4. C3×#5006 | C2 | semidirect |
| 5. C3×#4557 | C2 | semidirect |
| 7. #70547 | C3 | direct (N × H) |
| 23. C3×#424 | D3 | semidirect |
| 24. C3×#424 | C2×C3 | semidirect |
| 27. #5113 | C2×C3 | semidirect |
| 28. #5006 | C2×C3 | semidirect |
| 30. #4557 | C2×C3 | semidirect |
| 102. #424 | C3×D3 | semidirect |
| 282. C32 | #2053 | semidirect |
| 325. C3 | #70547 | direct (N × H) |
| 326. C3 | C3×#2053 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5748 | 2 |
| C32×#424 | 2 |
| C3×#5113 | 2 |
| C3×#5006 | 2 |
| C3×#4557 | 2 |
| C3×#2053 | 3 |
| #70547 | 3 |