Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
885 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 885 conjugacy classes of subgroups — too many to draw. Only its 156 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. #10591107 | C2 | semidirect |
| 5. #10589160 | C2 | semidirect |
| 12. #64145 | C4 | semidirect |
| 42. C2×#634 | C2×C4 | semidirect |
| 46. C4×C3⋊Dic3 | C2×C4 | semidirect |
| 323. C32 | #1885 | semidirect |
| 374. C3 | #70069 | semidirect |
| 375. C3 | #71649 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64145 | 2 |
| C3×#5798 | 2 |
| C2×C3×#833 | 2 |
| #10591107 | 2 |
| #10589160 | 2 |
| #71649 | 3 |
| #70069 | 3 |