Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1032 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 1032 conjugacy classes of subgroups — too many to draw. Only its 269 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 |
|---|---|---|
| 2. C2×C32×C4⋊C8 | C2 | semidirect |
| 4. C2×#63643 | C2 | semidirect |
| 5. C4×C4⋊(C3⋊Dic3) | C2 | semidirect |
| 16. #64084 | C4 | semidirect |
| 22. C2×C3×C4⋊C8 | D3 | semidirect |
| 93. C2×C4⋊C8 | C3⋊D3 | semidirect |
| 226. C32 | #1983 | semidirect |
| 277. C3 | #70458 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64084 | 2 |
| C2×C32×C4⋊C8 | 2 |
| C2×#63648 | 2 |
| C2×#63643 | 2 |
| C4×C4⋊(C3⋊Dic3) | 2 |
| #70458 | 3 |