Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
261 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 261 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
|---|---|---|
| 1. C2×C16×D9 | C2 | semidirect |
| 3. C4×C9×C16 | C2 | semidirect |
| 4. (C2×D9)⋊C16 | C2 | semidirect |
| 5. C4⋊(C9⋊C16) | C2 | semidirect |
| 32. C9×C16 | D4 | semidirect |
| 49. D36 | C16 | direct (N × H) |
| 60. C4×C16 | D9 | semidirect |
| 77. C2×D9 | C2×C16 | semidirect |
| 79. C4×C9 | C2×C16 | semidirect |
| 120. C16 | D36 | direct (N × H) |
| 130. C9 | D4×C16 | semidirect |
| 153. C4 | C16×D9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C16×D9 | 2 |
| C8×D36 | 2 |
| C4×C9×C16 | 2 |
| (C2×D9)⋊C16 | 2 |
| C4⋊(C9⋊C16) | 2 |
| C16×D12 | 3 |