Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
610 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 610 conjugacy classes of subgroups — too many to draw. Only its 106 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. C22×#3708 | C2 | semidirect |
| 3. #10590176 | C2 | direct (N × H) |
| 11. C2×#3708 | C22 | semidirect |
| 38. C22×C3⋊D3 | C16 | semidirect |
| 76. C2×C3⋊D3 | C2×C16 | semidirect |
| 106. C2×C32 | C22⋊C16 | semidirect |
| 138. C32 | C2×C22⋊C16 | semidirect |
| 175. C2 | #10590176 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×C3⋊D3 | 2 |
| C22×#3708 | 2 |
| #10590176 | 2 |
| C2×C22⋊C16 | 9 |