Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1080 conjugacy classes of subgroups; only the 361 normal subgroups are shown.
This group has 1080 conjugacy classes of subgroups — too many to draw. Only its 361 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. #10592764 | C2 | direct (N × H) |
| 130. C2×C32 | #499 | semidirect |
| 158. C32 | C2×#499 | semidirect |
| 172. C2×C3 | #5065 | semidirect |
| 184. C3 | C2×#5065 | semidirect |
| 185. C2 | #10592764 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×#125 | 2 |
| C2×#64079 | 2 |
| #10592764 | 2 |
| C2×#63635 | 2 |
| C2×#63634 | 2 |
| C2×C4×C3⋊(C3⋊C8) | 2 |
| C2×#5065 | 3 |