Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
449 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 449 conjugacy classes of subgroups — too many to draw. Only its 136 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 |
|---|---|---|
| 3. C3×C4⋊(C3⋊C16) | C2 | semidirect |
| 4. #10589133 | C2 | semidirect |
| 20. C4⋊(C3⋊C16) | D3 | semidirect |
| 62. C4×C3⋊D3 | C16 | semidirect |
| 109. C32×C4 | C2×C16 | semidirect |
| 114. C3⋊Dic3 | C2×C16 | semidirect |
| 159. C3⋊D3 | C4⋊C16 | semidirect |
| 188. C3×C4 | D3×C16 | semidirect |
| 197. C32 | C2×C4⋊C16 | semidirect |
| 230. C4 | #63542 | semidirect |
| 234. C3 | D3×C4⋊C16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C8×C3⋊D3 | 2 |
| C2×#63542 | 2 |
| C3×C4⋊(C3⋊C16) | 2 |
| #10589133 | 2 |
| D3×C4⋊C16 | 3 |