Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1080 conjugacy classes of subgroups; only the 345 normal subgroups are shown.
This group has 1080 conjugacy classes of subgroups — too many to draw. Only its 345 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. C2×#63656 | C2 | direct (N × H) |
| 13. #63656 | C22 | direct (N × H) |
| 72. C22×C32 | Q32 | semidirect |
| 98. C2×C32 | C2×Q32 | semidirect |
| 114. C22×C3 | #829 | semidirect |
| 120. C32 | C22×Q32 | semidirect |
| 132. C2×C3 | C2×#829 | semidirect |
| 134. C22 | #63656 | direct (N × H) |
| 140. C3 | C22×#829 | semidirect |
| 141. C2 | C2×#63656 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×Q16 | 2 |
| C22×#3746 | 2 |
| C2×#63656 | 2 |
| C22×C3⋊(C3⋊C16) | 2 |
| C22×#829 | 3 |