Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
741 conjugacy classes of subgroups; only the 188 normal subgroups are shown.
This group has 741 conjugacy classes of subgroups — too many to draw. Only its 188 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 |
|---|---|---|
| 16. #63561 | C4 | direct (N × H) |
| 130. C32×C4 | #101 | semidirect |
| 219. C3×C4 | #824 | semidirect |
| 226. C32 | C4×#101 | semidirect |
| 262. C4 | #63561 | direct (N × H) |
| 265. C3 | C4×#824 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#634 | 2 |
| C3×C4×#208 | 2 |
| C2×#63561 | 2 |
| #10589168 | 2 |
| C4×#824 | 3 |