Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
4872 conjugacy classes of subgroups; only the 1401 normal subgroups are shown.
This group has 4872 conjugacy classes of subgroups — too many to draw. Only its 1401 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×#64153 | C2 | direct (N × H) |
| 15. #64153 | C22 | direct (N × H) |
| 31. C22×C3⋊Dic3 | Q8 | semidirect |
| 59. C2×C3⋊Dic3 | C2×Q8 | semidirect |
| 83. C22×C32 | C4⋊Q8 | semidirect |
| 90. C3⋊Dic3 | C22×Q8 | semidirect |
| 115. C2×C32 | C2×C4⋊Q8 | semidirect |
| 133. C22×C3 | #944 | semidirect |
| 141. C32 | C22×C4⋊Q8 | semidirect |
| 155. C2×C3 | C2×#944 | semidirect |
| 158. C22 | #64153 | direct (N × H) |
| 166. C3 | C22×#944 | semidirect |
| 167. C2 | C2×#64153 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C32×Q8 | 2 |
| C23×#634 | 2 |
| C2×#64153 | 2 |
| C22×#3750 | 2 |
| C22×C4×C3⋊Dic3 | 2 |
| C22×#944 | 3 |