Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
417 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 417 conjugacy classes of subgroups — too many to draw. Only its 148 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 |
|---|---|---|
| 4. C3×Dic3×C16 | C2 | semidirect |
| 5. #10589103 | C2 | semidirect |
| 12. C16×C3⋊D3 | C4 | semidirect |
| 16. #63544 | C4 | semidirect |
| 23. Dic3×C16 | D3 | semidirect |
| 161. C32 | #2108 | semidirect |
| 186. C3 | #69051 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C16×C3⋊D3 | 2 |
| #10590700 | 2 |
| C2×#63544 | 2 |
| C3×Dic3×C16 | 2 |
| #10589103 | 2 |
| #69051 | 3 |