Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
355 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 355 conjugacy classes of subgroups — too many to draw. Only its 106 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 |
|---|---|---|
| 21. #63551 | C4 | direct (N × H) |
| 150. C32×C4 | Q32 | semidirect |
| 238. C3×C4 | Dic24 | semidirect |
| 239. C3×C4 | #829 | semidirect |
| 252. C32 | C4×Q32 | semidirect |
| 282. C4 | #63551 | direct (N × H) |
| 286. C3 | C4×Dic24 | semidirect |
| 287. C3 | C4×#829 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#3746 | 2 |
| C3×C4×Dic12 | 2 |
| C2×#63551 | 2 |
| C3×C4×C3⋊C16 | 2 |
| #10589139 | 2 |
| #10589119 | 2 |
| #10589118 | 2 |
| C4×#829 | 3 |
| C4×Dic24 | 3 |