Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
385 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 385 conjugacy classes of subgroups — too many to draw. Only its 78 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. C2×#63627 | C2 | semidirect |
| 2. #10590864 | C2 | semidirect |
| 3. #10590763 | C2 | semidirect |
| 5. C3×#4509 | C2 | semidirect |
| 6. C3×Dic3⋊C16 | C2 | semidirect |
| 7. #10589119 | C2 | semidirect |
| 34. #4509 | D3 | semidirect |
| 36. Dic3⋊C16 | D3 | semidirect |
| 288. C32 | #2210 | semidirect |
| 334. C3 | #69203 | semidirect |
| 335. C3 | #69288 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63627 | 2 |
| #10590864 | 2 |
| #10590763 | 2 |
| C2×#63546 | 2 |
| C3×#4509 | 2 |
| C3×Dic3⋊C16 | 2 |
| #10589119 | 2 |
| #69288 | 3 |
| #69203 | 3 |