Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
353 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 353 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
|---|---|---|
| 3. C3×#4505 | C2 | semidirect |
| 4. #10589140 | C2 | semidirect |
| 10. C16×C3⋊D3 | C4 | semidirect |
| 17. #4505 | D3 | semidirect |
| 132. C32 | #2158 | semidirect |
| 156. C3 | #69345 | 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 |
| #10590714 | 2 |
| C3×#4505 | 2 |
| #10589140 | 2 |
| #69345 | 3 |