Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
405 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 405 conjugacy classes of subgroups — too many to draw. Only its 88 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. #10592395 | C2 | semidirect |
| 2. C3×C4×D24 | C2 | semidirect |
| 3. C2×#63548 | C2 | semidirect |
| 5. C3×C4⋊(C3⋊C16) | C2 | semidirect |
| 6. #10589119 | C2 | semidirect |
| 7. #10589116 | C2 | semidirect |
| 31. C4×D24 | D3 | semidirect |
| 37. C4⋊(C3⋊C16) | D3 | semidirect |
| 298. C32 | #2210 | semidirect |
| 344. C3 | #69288 | semidirect |
| 345. C3 | #70890 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592395 | 2 |
| C3×C4×D24 | 2 |
| C2×#63548 | 2 |
| C2×#63546 | 2 |
| C3×C4⋊(C3⋊C16) | 2 |
| #10589119 | 2 |
| #10589116 | 2 |
| #70890 | 3 |
| #69288 | 3 |