Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
333 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 333 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 124. C32×C4 | Q32 | semidirect |
| 203. C3×C4 | #829 | semidirect |
| 204. C3×C4 | #829 | semidirect |
| 212. C32 | #2209 | semidirect |
| 240. C4 | #63550 | semidirect |
| 244. C3 | #70916 | semidirect |
| 245. C3 | #71316 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4699 | 2 |
| C3×C4×Dic12 | 2 |
| C2×#63550 | 2 |
| C4⋊(C3⋊(C3⋊C16)) | 2 |
| #10589117 | 2 |
| #71316 | 3 |
| #70916 | 3 |