Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
751 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 751 conjugacy classes of subgroups — too many to draw. Only its 148 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. C2×#63561 | C2 | semidirect |
| 5. #10589171 | C2 | semidirect |
| 331. C32 | #1915 | semidirect |
| 376. C3 | #70138 | semidirect |
| 377. C3 | #72031 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596296 | 2 |
| C3×#5819 | 2 |
| C3×#5237 | 2 |
| C2×#63561 | 2 |
| #10589171 | 2 |
| #72031 | 3 |
| #70138 | 3 |