Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
309 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 309 conjugacy classes of subgroups — too many to draw. Only its 108 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 |
|---|---|---|
| 171. C32 | #2241 | semidirect |
| 199. C3 | #71310 | semidirect |
| 200. C3 | #71382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4699 | 2 |
| C3×#4682 | 2 |
| C4×C3⋊(C3⋊C16) | 2 |
| #10589117 | 2 |
| #71382 | 3 |
| #71310 | 3 |