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. #10592550 | C2 | semidirect |
| 4. C8×#634 | C2 | semidirect |
| 5. C32×#334 | C2 | semidirect |
| 6. #10589352 | C2 | semidirect |
| 28. C3×#334 | D3 | semidirect |
| 81. #634 | SD16 | semidirect |
| 85. C32×C8 | SD16 | semidirect |
| 91. #334 | C3⋊D3 | semidirect |
| 159. C3×C8 | #204 | semidirect |
| 196. C32 | #1666 | semidirect |
| 217. C8 | #3744 | semidirect |
| 234. C3 | #68546 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592550 | 2 |
| #10592547 | 2 |
| #10592392 | 2 |
| C8×#634 | 2 |
| C32×#334 | 2 |
| #10589352 | 2 |
| #10589351 | 2 |
| #68546 | 3 |