Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
473 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 473 conjugacy classes of subgroups — too many to draw. Only its 168 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. #10589104 | C2 | semidirect |
| 14. #63544 | C4 | direct (N × H) |
| 20. C4×C3⋊C16 | D3 | semidirect |
| 32. C3×C3⋊C16 | C2×C4 | semidirect |
| 90. C3⋊C16 | C4×D3 | semidirect |
| 94. C32×C4 | M32 | semidirect |
| 156. C3×C4 | #798 | semidirect |
| 163. C32 | C4×M32 | semidirect |
| 187. C4 | #63544 | direct (N × H) |
| 191. C3 | C4×#798 | 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×#63544 | 2 |
| C3×C4×C3⋊C16 | 2 |
| #10589104 | 2 |
| C4×#798 | 3 |