Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1314 conjugacy classes of subgroups; only the 233 normal subgroups are shown.
This group has 1314 conjugacy classes of subgroups — too many to draw. Only its 233 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. #10596196 | C2 | semidirect |
| 2. #10596187 | C2 | semidirect |
| 3. C32×#492 | C2 | semidirect |
| 4. #10592871 | C2 | semidirect |
| 5. #10592864 | C2 | semidirect |
| 6. #10592778 | C2 | semidirect |
| 7. #10592772 | C2 | semidirect |
| 8. #10592393 | C2 | semidirect |
| 9. #10592384 | C2 | semidirect |
| 38. C3×#492 | D3 | semidirect |
| 135. #492 | C3⋊D3 | semidirect |
| 302. C32 | #3207 | semidirect |
| 355. C3 | #81765 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596196 | 2 |
| #10596187 | 2 |
| C32×#492 | 2 |
| #10592871 | 2 |
| #10592864 | 2 |
| #10592778 | 2 |
| #10592772 | 2 |
| #10592393 | 2 |
| #10592384 | 2 |
| #81765 | 3 |