Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
305 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 305 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 |
|---|---|---|
| 2. C3×#4683 | C2 | semidirect |
| 3. C4×C3⋊(C3⋊C16) | C2 | semidirect |
| 4. #10589117 | C2 | semidirect |
| 20. #4683 | D3 | semidirect |
| 183. C32 | #2242 | semidirect |
| 212. C3 | #71318 | semidirect |
| 213. C3 | #71351 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4696 | 2 |
| C3×#4683 | 2 |
| C4×C3⋊(C3⋊C16) | 2 |
| #10589117 | 2 |
| #10589114 | 2 |
| #71351 | 3 |
| #71318 | 3 |