Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
5160 conjugacy classes of subgroups; only the 2857 normal subgroups are shown.
This group has 5160 conjugacy classes of subgroups — too many to draw. Only its 2857 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×#3748 | C2 | direct (N × H) |
| 3. C23×C3⋊(C3⋊C8) | C2 | semidirect |
| 10. C2×#3748 | C22 | direct (N × H) |
| 11. C22×C3⋊(C3⋊C8) | C22 | semidirect |
| 23. #3748 | C23 | direct (N × H) |
| 24. C2×C3⋊(C3⋊C8) | C23 | semidirect |
| 34. C23×C32 | M16 | semidirect |
| 42. C3⋊(C3⋊C8) | C24 | semidirect |
| 57. C22×C32 | C2×M16 | semidirect |
| 71. C23×C3 | #208 | semidirect |
| 81. C2×C32 | C22×M16 | semidirect |
| 94. C22×C3 | C2×#208 | semidirect |
| 100. C32 | C23×M16 | semidirect |
| 102. C23 | #3748 | direct (N × H) |
| 112. C2×C3 | C22×#208 | semidirect |
| 115. C22 | C2×#3748 | direct (N × H) |
| 121. C3 | C23×#208 | semidirect |
| 123. C2 | C22×#3748 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C32×C4 | 2 |
| C22×#3748 | 2 |
| C23×C3⋊(C3⋊C8) | 2 |
| C23×#208 | 3 |