Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
329 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 329 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 14. C3×Dic24 | C4 | semidirect |
| 57. Dic24 | Dic3 | semidirect |
| 104. C3⋊Dic3 | Q32 | semidirect |
| 174. C32 | C4×Q32 | semidirect |
| 202. C3 | #69318 | semidirect |
| 203. C3 | Dic3×Q32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Dic24 | 2 |
| #10590818 | 2 |
| C16×C3⋊Dic3 | 2 |
| C3×#4504 | 2 |
| #10589117 | 2 |
| Dic3×Q32 | 3 |
| #69318 | 3 |