Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
411 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 411 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 |
|---|---|---|
| 4. #67691 | C3 | direct (N × H) |
| 6. C2×C32×M16 | C4 | semidirect |
| 7. C22×C32×C8 | C4 | semidirect |
| 11. C3×#834 | C4 | semidirect |
| 36. C2×C3×M16 | Dic3 | semidirect |
| 37. C2×C3×M16 | C3×C4 | semidirect |
| 39. C22×C3×C8 | Dic3 | semidirect |
| 40. C22×C3×C8 | C3×C4 | semidirect |
| 49. #834 | C3×C4 | semidirect |
| 117. C2×M16 | C3×Dic3 | semidirect |
| 118. C22×C8 | C3×Dic3 | semidirect |
| 214. C32 | #1391 | semidirect |
| 253. C3 | #67691 | direct (N × H) |
| 254. C3 | C3×#1391 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#408 | 2 |
| C3×#5240 | 2 |
| C3×#1391 | 3 |
| #67691 | 3 |