Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
600 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 81 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. #10593637 | C2 | direct (N × H) |
| 226. C2×C3 | #5403 | semidirect |
| 238. C3 | C2×#5403 | semidirect |
| 241. C2 | #10593637 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64265 | 2 |
| C2×C3×#131⋊C3 | 2 |
| #10593637 | 2 |
| C2×#5403 | 3 |
| C2×#5143 | 3 |
| C2×#3746 | 4 |