Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
172 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 58 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. #10589365 | C2 | semidirect |
| 3. C3×#4506 | C2 | semidirect |
| 15. #4506 | D3 | semidirect |
| 119. C32 | #1419 | semidirect |
| 141. C3 | #67583 | semidirect |
| 142. C3 | #67825 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D48 | 2 |
| #10589365 | 2 |
| C3×#4506 | 2 |
| #67825 | 3 |
| #67583 | 3 |