Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1032 conjugacy classes of subgroups; only the 313 normal subgroups are shown.
This group has 1032 conjugacy classes of subgroups — too many to draw. Only its 313 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. #10589417 | C2 | semidirect |
| 12. C2×C4⋊(C3⋊Dic3) | C4 | semidirect |
| 180. C32 | #1823 | semidirect |
| 223. C3 | #69924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊(C3⋊Dic3) | 2 |
| C2×C32×C22⋊C8 | 2 |
| #10592911 | 2 |
| #10589417 | 2 |
| #69924 | 3 |