Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
275 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 275 conjugacy classes of subgroups — too many to draw. Only its 74 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. C3×#4463 | C2 | semidirect |
| 4. #67787 | C3 | direct (N × H) |
| 14. #4463 | C2×C3 | semidirect |
| 144. C32 | #1359 | semidirect |
| 170. C3 | #67787 | direct (N × H) |
| 171. C3 | C3×#1359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#492 | 2 |
| C3×#4463 | 2 |
| C3×#1359 | 3 |
| #67787 | 3 |