Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
443 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 443 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 322. C32 | #2082 | semidirect |
| 367. C3 | #69023 | semidirect |
| 368. C3 | #70733 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592819 | 2 |
| C3×#5124 | 2 |
| #10591107 | 2 |
| C2×#63561 | 2 |
| C3×#4559 | 2 |
| #10589171 | 2 |
| #10589158 | 2 |
| #70733 | 3 |
| #69023 | 3 |