Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
518 conjugacy classes of subgroups; only the 199 normal subgroups are shown.
This group has 518 conjugacy classes of subgroups — too many to draw. Only its 199 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. C2×#64218 | C2 | semidirect |
| 3. #10596481 | C2 | direct (N × H) |
| 4. C2×#64214 | C2 | semidirect |
| 5. C2×#64213 | C2 | semidirect |
| 15. #64218 | C22 | semidirect |
| 16. C2×#3771 | C22 | semidirect |
| 17. #64214 | C22 | semidirect |
| 18. #64213 | C22 | semidirect |
| 41. #3771 | C23 | semidirect |
| 86. C2×C3⋊D3 | M32 | semidirect |
| 126. C2×C32 | C2×M32 | semidirect |
| 129. C3⋊D3 | C2×M32 | semidirect |
| 166. C32 | C22×M32 | semidirect |
| 212. C2 | #10596481 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3787 | 2 |
| C2×#64218 | 2 |
| #10596481 | 2 |
| C2×#64214 | 2 |
| C2×#64213 | 2 |
| C22×M32 | 9 |