Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
414 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 137 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. C32×#499 | C2 | semidirect |
| 3. #10589358 | C2 | semidirect |
| 5. C4×C3⋊(C3⋊C16) | C2 | semidirect |
| 16. C3×#499 | D3 | semidirect |
| 54. #499 | C3⋊D3 | semidirect |
| 122. C32 | #2242 | semidirect |
| 145. C3 | #71351 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#499 | 2 |
| #10592395 | 2 |
| #10589358 | 2 |
| #10589357 | 2 |
| C4×C3⋊(C3⋊C16) | 2 |
| #71351 | 3 |