Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1656 conjugacy classes of subgroups; only the 457 normal subgroups are shown.
This group has 1656 conjugacy classes of subgroups — too many to draw. Only its 457 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 |
|---|---|---|
| 4. #10592791 | C2 | direct (N × H) |
| 61. C2×C32×C4 | Q16 | semidirect |
| 98. C32×C4 | C2×Q16 | semidirect |
| 119. C2×C3×C4 | #216 | semidirect |
| 129. C2×C32 | #494 | semidirect |
| 154. C3×C4 | C2×#216 | semidirect |
| 157. C32 | C2×#494 | semidirect |
| 167. C2×C4 | #3756 | semidirect |
| 173. C2×C3 | #5092 | semidirect |
| 182. C4 | C2×#3756 | semidirect |
| 184. C3 | C2×#5092 | semidirect |
| 185. C2 | #10592791 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C4⋊Q8 | 2 |
| C22×#3756 | 2 |
| C2×#64078 | 2 |
| #10592791 | 2 |
| C2×C4×C3⋊(C3⋊C8) | 2 |
| C2×#5092 | 3 |