Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
681 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 681 conjugacy classes of subgroups — too many to draw. Only its 122 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 |
|---|---|---|
| 2. C2×C3×#827 | C2 | semidirect |
| 3. C3×#5116 | C2 | semidirect |
| 4. C3×#4562 | C2 | semidirect |
| 5. C3×#4549 | C2 | semidirect |
| 7. #72036 | C3 | direct (N × H) |
| 14. C2×C3×Dic12 | C22 | semidirect |
| 16. C3×#818 | C22 | semidirect |
| 18. C2×C3×C3⋊C16 | C22 | semidirect |
| 24. C2×#827 | C2×C3 | semidirect |
| 25. #5116 | C2×C3 | semidirect |
| 28. #4562 | C2×C3 | semidirect |
| 29. #4549 | C2×C3 | semidirect |
| 67. C2×Dic12 | C22×C3 | semidirect |
| 73. #818 | C22×C3 | semidirect |
| 75. C2×C3⋊C16 | C22×C3 | semidirect |
| 153. C22×C32 | SD32 | semidirect |
| 264. C22×C3 | #827 | semidirect |
| 265. C22×C3 | C3×SD32 | semidirect |
| 281. C32 | #2187 | semidirect |
| 321. C22 | C3×#827 | semidirect |
| 329. C3 | #72036 | direct (N × H) |
| 330. C3 | C3×#2187 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×D8 | 2 |
| C2×C3×#827 | 2 |
| C3×#5116 | 2 |
| C3×#4562 | 2 |
| C3×#4549 | 2 |
| C3×#2187 | 3 |
| #72036 | 3 |