Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1206 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 1206 conjugacy classes of subgroups — too many to draw. Only its 209 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. #10596100 | C2 | semidirect |
| 2. C32×#470 | C2 | semidirect |
| 3. #10592886 | C2 | semidirect |
| 4. #10592834 | C2 | semidirect |
| 5. #10592828 | C2 | semidirect |
| 6. #10592747 | C2 | semidirect |
| 7. #10592562 | C2 | semidirect |
| 8. #10592509 | C2 | semidirect |
| 9. #10592504 | C2 | semidirect |
| 37. C3×#470 | D3 | semidirect |
| 135. #470 | C3⋊D3 | semidirect |
| 297. C32 | #3204 | semidirect |
| 347. C3 | #80913 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596100 | 2 |
| C32×#470 | 2 |
| #10592886 | 2 |
| #10592834 | 2 |
| #10592828 | 2 |
| #10592747 | 2 |
| #10592562 | 2 |
| #10592509 | 2 |
| #10592504 | 2 |
| #80913 | 3 |