Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
358 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 122 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. #10590148 | C2 | semidirect |
| 4. C4×#3708 | C2 | semidirect |
| 8. #63773 | C4 | direct (N × H) |
| 26. #3708 | C2×C4 | semidirect |
| 67. C32×C4 | M32 | semidirect |
| 114. C32 | C4×M32 | semidirect |
| 134. C4 | #63773 | 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×C4×C3⋊(C3⋊C8) | 2 |
| #10590148 | 2 |
| C4×#3708 | 2 |
| C4×M32 | 9 |