Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2580 conjugacy classes of subgroups; only the 1582 normal subgroups are shown.
This group has 2580 conjugacy classes of subgroups — too many to draw. Only its 1582 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×#3667 | C2 | direct (N × H) |
| 3. C23×C9⋊C8 | C2 | semidirect |
| 10. C2×#3667 | C22 | direct (N × H) |
| 11. C22×C9⋊C8 | C22 | semidirect |
| 23. #3667 | C23 | direct (N × H) |
| 24. C2×C9⋊C8 | C23 | semidirect |
| 34. C23×C9 | M16 | semidirect |
| 42. C9⋊C8 | C24 | semidirect |
| 57. C22×C9 | C2×M16 | semidirect |
| 81. C2×C9 | C22×M16 | semidirect |
| 100. C9 | C23×M16 | semidirect |
| 102. C23 | #3667 | direct (N × H) |
| 115. C22 | C2×#3667 | direct (N × H) |
| 123. C2 | C22×#3667 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C4×C9 | 2 |
| C22×#3667 | 2 |
| C23×C9⋊C8 | 2 |
| C23×#208 | 3 |