Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
552 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 209 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. C32×C4×C16 | C2 | semidirect |
| 5. #10589368 | C2 | semidirect |
| 6. C16×C3⋊Dic3 | C2 | semidirect |
| 7. #10589327 | C2 | semidirect |
| 20. #63625 | C4 | semidirect |
| 21. C16×C3⋊D3 | C4 | semidirect |
| 25. C3×C4×C16 | D3 | semidirect |
| 77. C4×C16 | C3⋊D3 | semidirect |
| 154. C32 | #2108 | semidirect |
| 178. C3 | #69051 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63625 | 2 |
| C2×C16×C3⋊D3 | 2 |
| #10592388 | 2 |
| C32×C4×C16 | 2 |
| #10589368 | 2 |
| C16×C3⋊Dic3 | 2 |
| #10589327 | 2 |
| #69051 | 3 |