Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
481 conjugacy classes of subgroups; only the 180 normal subgroups are shown.
This group has 481 conjugacy classes of subgroups — too many to draw. Only its 180 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 |
|---|---|---|
| 4. C3×Dic3×C16 | C2 | semidirect |
| 5. Dic3×C3⋊C16 | C2 | semidirect |
| 12. C16×C3⋊D3 | C4 | semidirect |
| 16. #63542 | C4 | semidirect |
| 23. Dic3×C16 | D3 | semidirect |
| 35. C32×C16 | C2×C4 | semidirect |
| 36. C3⋊(C3⋊C16) | C2×C4 | semidirect |
| 37. C3×C3⋊C16 | C2×C4 | semidirect |
| 62. #624 | C16 | direct (N × H) |
| 91. C3×C16 | C4×D3 | semidirect |
| 94. C3⋊C16 | C4×D3 | semidirect |
| 101. C3×Dic3 | C2×C16 | semidirect |
| 135. C3⋊D3 | C4×C16 | semidirect |
| 148. C16 | #624 | direct (N × H) |
| 162. Dic3 | D3×C16 | semidirect |
| 163. C32 | C2×C4×C16 | semidirect |
| 189. C3 | C4×D3×C16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C16×C3⋊D3 | 2 |
| C8×#624 | 2 |
| C2×#63542 | 2 |
| C3×Dic3×C16 | 2 |
| Dic3×C3⋊C16 | 2 |
| C4×D3×C16 | 3 |