Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
462 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 121 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. C32×#444 | C2 | semidirect |
| 3. #10592410 | C2 | semidirect |
| 4. #10589432 | C2 | semidirect |
| 5. #10589361 | C2 | semidirect |
| 6. #10589360 | C2 | semidirect |
| 7. #10589332 | C2 | semidirect |
| 16. #63655 | C4 | semidirect |
| 17. #63653 | C4 | semidirect |
| 22. C3×#444 | D3 | semidirect |
| 32. C32×Q16 | C2×C4 | semidirect |
| 34. C32×D8 | C2×C4 | semidirect |
| 46. C3⋊(C3⋊C16) | C2×C4 | semidirect |
| 77. #444 | C3⋊D3 | semidirect |
| 86. C3×Q16 | C4×D3 | semidirect |
| 88. C3×D8 | C4×D3 | semidirect |
| 146. Q16 | C4×C3⋊D3 | semidirect |
| 150. D8 | C4×C3⋊D3 | semidirect |
| 171. C32 | AGL(1,ℤ/16) | semidirect |
| 201. C3 | #70929 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#444 | 2 |
| #10592892 | 2 |
| #10592410 | 2 |
| #10589432 | 2 |
| #10589361 | 2 |
| #10589360 | 2 |
| #10589332 | 2 |
| #70929 | 3 |