Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
519 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 519 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 |
|---|---|---|
| 1. C22×C3×Dic12 | C2 | semidirect |
| 3. C2×C3×#827 | C2 | semidirect |
| 4. C3×#4549 | C2 | semidirect |
| 5. C3×#4492 | C2 | semidirect |
| 7. #71077 | C3 | direct (N × H) |
| 20. C22×Dic12 | C2×C3 | semidirect |
| 25. C2×#827 | C2×C3 | semidirect |
| 28. #4549 | C2×C3 | semidirect |
| 29. #4492 | C2×C3 | semidirect |
| 46. C3×Dic12 | D4 | semidirect |
| 140. Dic12 | C3×D4 | semidirect |
| 148. C22×C32 | SD32 | semidirect |
| 252. C22×C3 | #827 | semidirect |
| 253. C22×C3 | C3×SD32 | semidirect |
| 270. C32 | #2185 | semidirect |
| 308. C22 | C3×#827 | semidirect |
| 316. C3 | #71077 | direct (N × H) |
| 317. C3 | C3×#2185 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×Dic12 | 2 |
| C32×#466 | 2 |
| C2×C3×#827 | 2 |
| C3×#4549 | 2 |
| C3×#4492 | 2 |
| C3×#2185 | 3 |
| #71077 | 3 |