Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
486 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 127 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. #10592572 | C2 | semidirect |
| 5. #10589369 | C2 | semidirect |
| 6. C16×C3⋊Dic3 | C2 | semidirect |
| 7. #10589356 | C2 | semidirect |
| 16. #63654 | C4 | semidirect |
| 42. #3746 | C2×C4 | semidirect |
| 44. C3⋊(C3⋊C16) | C2×C4 | semidirect |
| 107. C3⋊Dic3 | SD32 | semidirect |
| 167. C32 | C4×SD32 | semidirect |
| 198. C3 | #69175 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×C3⋊Dic3 | 2 |
| C2×#63654 | 2 |
| #10592572 | 2 |
| C32×#357 | 2 |
| #10589369 | 2 |
| C16×C3⋊Dic3 | 2 |
| #10589356 | 2 |
| #69175 | 3 |