Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
257 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 257 conjugacy classes of subgroups — too many to draw. Only its 76 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×C3×D48 | C2 | semidirect |
| 2. C2×C3⋊(C3⋊C32) | C2 | semidirect |
| 3. #10589070 | C2 | direct (N × H) |
| 8. C3×D48 | C22 | semidirect |
| 9. C3⋊(C3⋊C32) | C22 | semidirect |
| 11. C2×D48 | D3 | semidirect |
| 29. D48 | C2×D3 | semidirect |
| 75. C2×C32 | D32 | semidirect |
| 94. C32 | C2×D32 | semidirect |
| 104. C2×C3 | #4519 | semidirect |
| 113. C3 | C2×#4519 | semidirect |
| 115. C2 | #10589070 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D48 | 2 |
| C2×C3⋊(C3⋊C32) | 2 |
| #10589070 | 2 |
| C2×#4519 | 3 |