Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
657 conjugacy classes of subgroups; only the 212 normal subgroups are shown.
This group has 657 conjugacy classes of subgroups — too many to draw. Only its 212 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 |
|---|---|---|
| 3. #10589096 | C2 | direct (N × H) |
| 147. C2×C32 | #333 | semidirect |
| 185. C32 | C2×#333 | semidirect |
| 202. C2×C3 | #4481 | semidirect |
| 216. C3 | C2×#4481 | semidirect |
| 217. C2 | #10589096 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64078 | 2 |
| C2×C3×C4⋊(C3⋊C8) | 2 |
| #10589096 | 2 |
| C2×#4481 | 3 |