Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
948 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 948 conjugacy classes of subgroups — too many to draw. Only its 185 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×#407 | C2 | semidirect |
| 3. #10592906 | C2 | semidirect |
| 4. #10589335 | C2 | semidirect |
| 5. #10589334 | C2 | semidirect |
| 25. C3×#407 | D3 | semidirect |
| 89. C22×C3⋊D3 | M16 | semidirect |
| 108. C2×C3⋊Dic3 | M16 | semidirect |
| 115. #407 | C3⋊D3 | semidirect |
| 290. C32 | #1465 | semidirect |
| 359. C3 | #69968 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#638 | 2 |
| C32×#407 | 2 |
| #10592906 | 2 |
| #10589335 | 2 |
| #10589334 | 2 |
| #69968 | 3 |