Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
733 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 733 conjugacy classes of subgroups — too many to draw. Only its 148 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 |
|---|---|---|
| 2. C2×C3×#803 | C2 | semidirect |
| 3. #10589087 | C2 | direct (N × H) |
| 14. C3×#803 | C22 | semidirect |
| 18. C2×#803 | D3 | semidirect |
| 59. #803 | C2×D3 | semidirect |
| 177. C2×C32 | #329 | semidirect |
| 224. C32 | C2×#329 | semidirect |
| 245. C2×C3 | #4464 | semidirect |
| 263. C3 | C2×#4464 | semidirect |
| 265. C2 | #10589087 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64084 | 2 |
| C2×C3×#803 | 2 |
| #10589087 | 2 |
| C2×#4464 | 3 |