Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
477 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 477 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. C32×#493 | C2 | semidirect |
| 2. C3×#5072 | C2 | semidirect |
| 3. C3×#4688 | C2 | semidirect |
| 4. C3×#4544 | C2 | semidirect |
| 5. C3×#4457 | C2 | semidirect |
| 7. #71283 | C3 | direct (N × H) |
| 20. C3×#493 | D3 | semidirect |
| 21. C3×#493 | C2×C3 | semidirect |
| 24. #5072 | C2×C3 | semidirect |
| 25. #4688 | C2×C3 | semidirect |
| 28. #4544 | C2×C3 | semidirect |
| 29. #4457 | C2×C3 | semidirect |
| 88. C32×C8 | D8 | semidirect |
| 91. #493 | C3×D3 | semidirect |
| 202. C3×C8 | #213 | semidirect |
| 203. C3×C8 | C3×D8 | semidirect |
| 259. C32 | #1687 | semidirect |
| 277. C8 | C3×#213 | semidirect |
| 305. C3 | #71283 | direct (N × H) |
| 306. C3 | C3×#1687 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#493 | 2 |
| C3×#5072 | 2 |
| C3×#4688 | 2 |
| C3×#4544 | 2 |
| C3×#4457 | 2 |
| C3×#1687 | 3 |
| #71283 | 3 |