Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
929 conjugacy classes of subgroups; only the 316 normal subgroups are shown.
This group has 929 conjugacy classes of subgroups — too many to draw. Only its 316 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. #10590309 | C2 | direct (N × H) |
| 28. C2×C3⋊(C3⋊C8) | Q8 | semidirect |
| 60. C3⋊(C3⋊C8) | C2×Q8 | semidirect |
| 128. C2×C32 | #498 | semidirect |
| 159. C32 | C2×#498 | semidirect |
| 173. C2×C3 | #5080 | semidirect |
| 185. C3 | C2×#5080 | semidirect |
| 186. C2 | #10590309 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#869 | 2 |
| C2×C4×C3⋊(C3⋊C8) | 2 |
| C2×#63574 | 2 |
| #10590309 | 2 |
| C2×#5080 | 3 |