Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
486 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 486 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. Q16×C3⋊Dic3 | C2 | semidirect |
| 4. #10589430 | C2 | semidirect |
| 6. #10589371 | C2 | semidirect |
| 7. C16×C3⋊Dic3 | C2 | semidirect |
| 13. C32×SD32 | C4 | semidirect |
| 32. C32×Q16 | C2×C4 | semidirect |
| 43. C32×C16 | C2×C4 | semidirect |
| 50. C3×SD32 | Dic3 | semidirect |
| 84. C3×Q16 | C2×Dic3 | semidirect |
| 95. C3×C16 | C2×Dic3 | semidirect |
| 107. C3⋊Dic3 | SD32 | direct (N × H) |
| 112. SD32 | C3⋊Dic3 | direct (N × H) |
| 143. Q16 | C2×C3⋊Dic3 | semidirect |
| 155. C16 | C2×C3⋊Dic3 | semidirect |
| 167. C32 | C4×SD32 | semidirect |
| 198. C3 | Dic3×SD32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×SD32 | 2 |
| Q16×C3⋊Dic3 | 2 |
| D8×C3⋊Dic3 | 2 |
| #10589430 | 2 |
| #10589428 | 2 |
| #10589371 | 2 |
| C16×C3⋊Dic3 | 2 |
| Dic3×SD32 | 3 |