Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
573 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 573 conjugacy classes of subgroups — too many to draw. Only its 106 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. #10590625 | C2 | semidirect |
| 3. C3×#4553 | C2 | semidirect |
| 4. #10589110 | C2 | semidirect |
| 22. #4553 | D3 | semidirect |
| 262. C32 | #2115 | semidirect |
| 308. C3 | #69119 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64116 | 2 |
| #10590625 | 2 |
| C3×#4553 | 2 |
| #10589110 | 2 |
| #69119 | 3 |