Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
450 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 189 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 |
|---|---|---|
| 2. #10596487 | C2 | semidirect |
| 3. #10596485 | C2 | semidirect |
| 4. #10596481 | C2 | semidirect |
| 5. C2×#64213 | C2 | semidirect |
| 13. #64218 | C22 | semidirect |
| 14. C2×#3771 | C22 | semidirect |
| 15. #64214 | C22 | semidirect |
| 18. #64213 | C22 | semidirect |
| 103. C3⋊D3 | #504 | semidirect |
| 130. C32 | C2×#504 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596647 | 2 |
| #10596487 | 2 |
| #10596485 | 2 |
| #10596481 | 2 |
| C2×#64213 | 2 |
| C2×#504 | 9 |