Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
294 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 126 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. D4×C9⋊C8 | C2 | semidirect |
| 3. D4⋊(C9⋊C8) | C2 | semidirect |
| 4. #10588135 | C2 | semidirect |
| 5. C8×C9⋊C8 | C2 | semidirect |
| 24. C9×D8 | C8 | semidirect |
| 48. D4×C9 | C2×C8 | semidirect |
| 56. C8×C9 | C2×C8 | semidirect |
| 60. C9⋊C8 | D8 | direct (N × H) |
| 120. D8 | C9⋊C8 | direct (N × H) |
| 141. C9 | C8×D8 | semidirect |
| 144. D4 | C2×C9⋊C8 | semidirect |
| 156. C8 | C2×C9⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C9×D8 | 2 |
| D4×C9⋊C8 | 2 |
| D4⋊(C9⋊C8) | 2 |
| #10588135 | 2 |
| C8×C9⋊C8 | 2 |
| D8×C3⋊C8 | 3 |