Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
801 conjugacy classes of subgroups; only the 252 normal subgroups are shown.
This group has 801 conjugacy classes of subgroups — too many to draw. Only its 252 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 |
|---|---|---|
| 5. #10590874 | C2 | direct (N × H) |
| 134. C2×C32 | #499 | semidirect |
| 165. C32 | C2×#499 | semidirect |
| 180. C2×C3 | #4858 | semidirect |
| 192. C3 | C2×#4858 | semidirect |
| 193. C2 | #10590874 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63872 | 2 |
| C2×C8×C3⋊Dic3 | 2 |
| C2×C3×#817 | 2 |
| C2×#63576 | 2 |
| #10590874 | 2 |
| C2×#4858 | 3 |