Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
314 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 3. #10590179 | C2 | direct (N × H) |
| 7. #63773 | C4 | semidirect |
| 9. C2×#3708 | C4 | semidirect |
| 24. #3708 | C2×C4 | semidirect |
| 88. C2×C32 | #347 | semidirect |
| 111. C32 | C2×#347 | semidirect |
| 140. C2 | #10590179 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63773 | 2 |
| C2×#63642 | 2 |
| #10590179 | 2 |
| C2×#347 | 9 |