Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
738 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 218 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. C22×#3708 | C2 | semidirect |
| 3. C2×#63765 | C2 | direct (N × H) |
| 9. C2×#3708 | C22 | semidirect |
| 10. #63765 | C22 | direct (N × H) |
| 22. #3708 | C23 | semidirect |
| 53. C22×C32 | M32 | semidirect |
| 78. C2×C32 | C2×M32 | semidirect |
| 99. C32 | C22×M32 | semidirect |
| 116. C22 | #63765 | direct (N × H) |
| 123. C2 | C2×#63765 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×C3⋊D3 | 2 |
| C22×#3708 | 2 |
| C2×#63765 | 2 |
| C22×M32 | 9 |