Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
444 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 105 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×C32×D16 | C2 | semidirect |
| 2. #10592859 | C2 | semidirect |
| 3. #10592600 | C2 | semidirect |
| 4. #10589429 | C2 | semidirect |
| 5. #10589372 | C2 | semidirect |
| 18. C2×C3×D16 | D3 | semidirect |
| 61. C2×D16 | C3⋊D3 | semidirect |
| 135. C32 | #2221 | semidirect |
| 159. C3 | #71472 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×D16 | 2 |
| #10592859 | 2 |
| #10592600 | 2 |
| #10589429 | 2 |
| #10589372 | 2 |
| #71472 | 3 |