Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
516 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 141 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×#500 | C2 | semidirect |
| 4. #10589413 | C2 | semidirect |
| 5. #10589324 | C2 | semidirect |
| 18. C3×#500 | D3 | semidirect |
| 62. C32×C8 | SD16 | semidirect |
| 65. #500 | C3⋊D3 | semidirect |
| 119. C3×C8 | #215 | semidirect |
| 151. C32 | #1673 | semidirect |
| 167. C8 | #3755 | semidirect |
| 183. C3 | #71371 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#500 | 2 |
| #10592782 | 2 |
| C8×C4⋊(C3⋊D3) | 2 |
| #10589413 | 2 |
| #10589324 | 2 |
| #71371 | 3 |