Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
450 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 191 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 | direct (N × H) |
| 3. C2×#64214 | C2 | semidirect |
| 4. C2×#64213 | C2 | semidirect |
| 12. #64214 | C22 | semidirect |
| 13. #64213 | C22 | semidirect |
| 69. C2×C32 | #504 | semidirect |
| 90. C32 | C2×#504 | semidirect |
| 112. C2 | #10596487 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64289 | 2 |
| #10596487 | 2 |
| C2×#64214 | 2 |
| C2×#64213 | 2 |
| C2×#504 | 9 |