Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1545 conjugacy classes of subgroups; only the 426 normal subgroups are shown.
This group has 1545 conjugacy classes of subgroups — too many to draw. Only its 426 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. C3×#5220 | C2 | semidirect |
| 3. C3×#4937 | C2 | semidirect |
| 5. #83174 | C3 | direct (N × H) |
| 8. C32×#127 | C4 | semidirect |
| 17. #5220 | C2×C3 | semidirect |
| 18. #4937 | C2×C3 | semidirect |
| 22. C2×C32×D4 | C2×C4 | semidirect |
| 26. C32×C42 | C2×C4 | semidirect |
| 35. C3×#127 | Dic3 | semidirect |
| 36. C3×#127 | C3×C4 | semidirect |
| 66. C2×C3×D4 | C2×Dic3 | semidirect |
| 67. C2×C3×D4 | C2×C3×C4 | semidirect |
| 77. C3×C42 | C2×Dic3 | semidirect |
| 78. C3×C42 | C2×C3×C4 | semidirect |
| 89. #127 | C3×Dic3 | semidirect |
| 124. C2×D4 | C2×C3×Dic3 | semidirect |
| 129. C42 | C2×C3×Dic3 | semidirect |
| 150. C32 | #2380 | semidirect |
| 177. C3 | #83174 | direct (N × H) |
| 178. C3 | C3×#2380 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×#127 | 2 |
| C3×#5220 | 2 |
| C3×#4937 | 2 |
| C3×#2380 | 3 |
| #83174 | 3 |