Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
319 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 319 conjugacy classes of subgroups — too many to draw. Only its 92 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 |
|---|---|---|
| 1. #10592382 | C2 | semidirect |
| 3. C3×C4×C3⋊C16 | C2 | semidirect |
| 4. #10589118 | C2 | semidirect |
| 27. C4×C3⋊C16 | D3 | semidirect |
| 188. C32 | #2242 | semidirect |
| 217. C3 | #69059 | semidirect |
| 218. C3 | #71318 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592382 | 2 |
| C3×#4696 | 2 |
| C3×C4×C3⋊C16 | 2 |
| #10589118 | 2 |
| #10589115 | 2 |
| #71318 | 3 |
| #69059 | 3 |