Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
413 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 413 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
|---|---|---|
| 310. C32 | #2082 | semidirect |
| 355. C3 | #70342 | semidirect |
| 356. C3 | #70733 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5124 | 2 |
| C3×#5120 | 2 |
| #10591100 | 2 |
| C2×#63560 | 2 |
| #10589425 | 2 |
| #10589169 | 2 |
| #10589158 | 2 |
| #70733 | 3 |
| #70342 | 3 |