Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
432 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 125 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×#504 | C2 | semidirect |
| 2. #10592842 | C2 | semidirect |
| 4. C2×#63627 | C2 | semidirect |
| 5. #10589383 | C2 | semidirect |
| 6. #10589382 | C2 | semidirect |
| 7. #10589372 | C2 | semidirect |
| 24. C3×#504 | D3 | semidirect |
| 84. #504 | C3⋊D3 | semidirect |
| 181. C32 | #2223 | semidirect |
| 210. C3 | #71455 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#504 | 2 |
| #10592842 | 2 |
| #10592841 | 2 |
| C2×#63627 | 2 |
| #10589383 | 2 |
| #10589382 | 2 |
| #10589372 | 2 |
| #71455 | 3 |