Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
423 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 423 conjugacy classes of subgroups — too many to draw. Only its 110 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. C3×#4843 | C2 | semidirect |
| 2. C3×#4695 | C2 | semidirect |
| 3. C3×#4688 | C2 | semidirect |
| 4. C32×#334 | C2 | semidirect |
| 5. C3×#4485 | C2 | semidirect |
| 7. #68540 | C3 | direct (N × H) |
| 22. #4843 | C2×C3 | semidirect |
| 23. #4695 | C2×C3 | semidirect |
| 24. #4688 | C2×C3 | semidirect |
| 26. C3×#334 | D3 | semidirect |
| 27. C3×#334 | C2×C3 | semidirect |
| 29. #4485 | C2×C3 | semidirect |
| 87. C32×C8 | D8 | semidirect |
| 92. #334 | C3×D3 | semidirect |
| 192. C3×C8 | D24 | semidirect |
| 193. C3×C8 | C3×D8 | semidirect |
| 245. C32 | #1687 | semidirect |
| 263. C8 | C3×D24 | semidirect |
| 290. C3 | #68540 | direct (N × H) |
| 291. C3 | C3×#1687 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4843 | 2 |
| C3×#4695 | 2 |
| C3×#4688 | 2 |
| C32×#334 | 2 |
| C3×#4485 | 2 |
| C3×#1687 | 3 |
| #68540 | 3 |