Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
522 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 167 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. D8×C3⋊Dic3 | C2 | semidirect |
| 3. #10589428 | C2 | semidirect |
| 4. #10589370 | C2 | semidirect |
| 5. C16×C3⋊Dic3 | C2 | semidirect |
| 9. C32×D16 | C4 | semidirect |
| 23. C32×D8 | C2×C4 | semidirect |
| 29. C32×C16 | C2×C4 | semidirect |
| 34. C3×D16 | Dic3 | semidirect |
| 59. C3×D8 | C2×Dic3 | semidirect |
| 65. C3×C16 | C2×Dic3 | semidirect |
| 75. C3⋊Dic3 | D16 | direct (N × H) |
| 78. D16 | C3⋊Dic3 | direct (N × H) |
| 102. D8 | C2×C3⋊Dic3 | semidirect |
| 109. C16 | C2×C3⋊Dic3 | semidirect |
| 119. C32 | C4×D16 | semidirect |
| 144. C3 | Dic3×D16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×D16 | 2 |
| D8×C3⋊Dic3 | 2 |
| #10589428 | 2 |
| #10589370 | 2 |
| C16×C3⋊Dic3 | 2 |
| Dic3×D16 | 3 |