Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
886 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 886 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 |
|---|---|---|
| 2. C42×C22⋊C9 | C2 | semidirect |
| 3. C4×(C22⋊C9)⋊C4 | C2 | semidirect |
| 8. C4×(C22⋊C9)⋊C2 | C4 | direct (N × H) |
| 20. C4×C22⋊C9 | C2×C4 | semidirect |
| 21. (C22⋊C9)⋊C4 | C2×C4 | semidirect |
| 43. (C22⋊C9)⋊C2 | C42 | direct (N × H) |
| 49. C22×C42 | D9 | semidirect |
| 82. C22⋊C9 | C2×C42 | semidirect |
| 139. C22×C4 | C4×D9 | semidirect |
| 150. C42 | (C22⋊C9)⋊C2 | direct (N × H) |
| 199. C22 | C42×D9 | semidirect |
| 205. C4 | C4×(C22⋊C9)⋊C2 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×(C22⋊C9)⋊C2 | 2 |
| C42×C22⋊C9 | 2 |
| C4×(C22⋊C9)⋊C4 | 2 |
| C42×#67 | 3 |
| C42×D9 | 4 |