Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1050 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 1050 conjugacy classes of subgroups — too many to draw. Only its 205 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. #10596242 | C2 | semidirect |
| 2. C32×#508 | C2 | semidirect |
| 3. #10592894 | C2 | semidirect |
| 4. C3⋊D3×Q32 | C2 | semidirect |
| 5. #10592614 | C2 | semidirect |
| 6. #10592611 | C2 | semidirect |
| 7. C2×#63628 | C2 | semidirect |
| 8. #10592600 | C2 | semidirect |
| 30. C3×#508 | D3 | semidirect |
| 102. #508 | C3⋊D3 | semidirect |
| 208. C32 | #3417 | semidirect |
| 240. C3 | #82033 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596242 | 2 |
| C32×#508 | 2 |
| #10592894 | 2 |
| C3⋊D3×Q32 | 2 |
| #10592614 | 2 |
| #10592611 | 2 |
| C2×#63628 | 2 |
| #10592600 | 2 |
| #82033 | 3 |