Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
473 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 473 conjugacy classes of subgroups — too many to draw. Only its 156 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×#4461 | C2 | semidirect |
| 4. #10589102 | C2 | semidirect |
| 14. #63544 | C4 | semidirect |
| 20. #4461 | D3 | semidirect |
| 32. C3×C3⋊C16 | C2×C4 | semidirect |
| 90. C3⋊C16 | C4×D3 | semidirect |
| 98. C3⋊Dic3 | M32 | semidirect |
| 163. C32 | C4×M32 | semidirect |
| 191. C3 | #69071 | 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×#4461 | 2 |
| #10589102 | 2 |
| #69071 | 3 |