Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
262 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 75 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. A4×C3⋊C16 | C2 | direct (N × H) |
| 3. C23×C3⋊C16 | C3 | semidirect |
| 15. C22×C3⋊C16 | C2×C3 | semidirect |
| 42. C2×C3⋊C16 | A4 | direct (N × H) |
| 43. C2×C3×A4 | C16 | semidirect |
| 79. C3⋊C16 | C2×A4 | direct (N × H) |
| 81. C3×A4 | C2×C16 | semidirect |
| 100. C23×C3 | C3×C16 | semidirect |
| 104. C2×A4 | C3⋊C16 | direct (N × H) |
| 154. C22×C3 | C2×C3×C16 | semidirect |
| 157. A4 | C2×C3⋊C16 | direct (N × H) |
| 170. C23 | C3×C3⋊C16 | semidirect |
| 192. C2×C3 | A4×C16 | semidirect |
| 201. C22 | C2×C3×C3⋊C16 | semidirect |
| 209. C3 | C2×A4×C16 | semidirect |
| 213. C2 | A4×C3⋊C16 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C8×A4 | 2 |
| A4×C3⋊C16 | 2 |
| C23×C3⋊C16 | 3 |
| C2×A4×C16 | 3 |
| C2×C3×C3⋊C16 | 4 |