Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
642 conjugacy classes of subgroups; only the 281 normal subgroups are shown.
This group has 642 conjugacy classes of subgroups — too many to draw. Only its 281 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 |
|---|---|---|
| 3. #10589321 | C2 | semidirect |
| 4. #10589320 | C2 | semidirect |
| 5. C8×C3⋊(C3⋊C8) | C2 | semidirect |
| 50. C32×C8 | M16 | semidirect |
| 52. C3⋊(C3⋊C8) | M16 | semidirect |
| 93. C3×C8 | #208 | semidirect |
| 117. C32 | #1455 | semidirect |
| 128. C8 | #3748 | semidirect |
| 139. C3 | #69849 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C4×M16 | 2 |
| C4×#3748 | 2 |
| #10589321 | 2 |
| #10589320 | 2 |
| C8×C3⋊(C3⋊C8) | 2 |
| #69849 | 3 |