Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
465 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 465 conjugacy classes of subgroups — too many to draw. Only its 114 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. C2×C3×Dic24 | C2 | semidirect |
| 5. C3×#4503 | C2 | semidirect |
| 7. #69113 | C3 | direct (N × H) |
| 24. C2×Dic24 | C2×C3 | semidirect |
| 29. #4503 | C2×C3 | semidirect |
| 137. C22×C32 | Q32 | semidirect |
| 225. C22×C3 | Dic24 | semidirect |
| 226. C22×C3 | C3×Q32 | semidirect |
| 244. C32 | #2188 | semidirect |
| 275. C22 | C3×Dic24 | semidirect |
| 284. C3 | #69113 | direct (N × H) |
| 285. C3 | C3×#2188 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×Dic12 | 2 |
| C3×#5116 | 2 |
| C2×C3×Dic24 | 2 |
| C32×C22⋊C16 | 2 |
| C3×#4503 | 2 |
| C3×#2188 | 3 |
| #69113 | 3 |