Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
363 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 363 conjugacy classes of subgroups — too many to draw. Only its 114 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 |
|---|---|---|
| 7. #70916 | C3 | direct (N × H) |
| 134. C32×C4 | Q32 | semidirect |
| 219. C3×C4 | #829 | semidirect |
| 220. C3×C4 | C3×Q32 | semidirect |
| 226. C32 | #2209 | semidirect |
| 254. C4 | C3×#829 | semidirect |
| 258. C3 | #70916 | direct (N × H) |
| 259. C3 | C3×#2209 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C4×Q16 | 2 |
| C2×C3×#829 | 2 |
| C3×#4699 | 2 |
| C3×#4492 | 2 |
| C3×C4⋊(C3⋊C16) | 2 |
| C3×#2209 | 3 |
| #70916 | 3 |