Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1272 conjugacy classes of subgroups; only the 377 normal subgroups are shown.
This group has 1272 conjugacy classes of subgroups — too many to draw. Only its 377 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 |
|---|---|---|
| 6. #10592554 | C2 | direct (N × H) |
| 33. C2×C32×C8 | Q8 | semidirect |
| 42. C2×C3⋊(C3⋊C8) | Q8 | semidirect |
| 70. C32×C8 | C2×Q8 | semidirect |
| 71. C3⋊(C3⋊C8) | C2×Q8 | semidirect |
| 84. C2×C3×C8 | Dic6 | semidirect |
| 129. C3×C8 | C2×Dic6 | semidirect |
| 131. C2×C32 | #498 | semidirect |
| 142. C2×C8 | #634 | semidirect |
| 160. C32 | C2×#498 | semidirect |
| 174. C8 | C2×#634 | semidirect |
| 175. C2×C3 | #4855 | semidirect |
| 187. C3 | C2×#4855 | semidirect |
| 188. C2 | #10592554 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64097 | 2 |
| C2×C32×#106 | 2 |
| C2×#63644 | 2 |
| C2×C8×C3⋊Dic3 | 2 |
| C2×#63635 | 2 |
| #10592554 | 2 |
| C2×#4855 | 3 |