Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
305 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 305 conjugacy classes of subgroups — too many to draw. Only its 80 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. #10590873 | C2 | semidirect |
| 3. #10589430 | C2 | semidirect |
| 4. C3×#4564 | C2 | semidirect |
| 7. Dic3×C3⋊C16 | C2 | semidirect |
| 29. #4564 | D3 | semidirect |
| 249. C32 | #2242 | semidirect |
| 287. C3 | #69216 | semidirect |
| 288. C3 | #71318 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5191 | 2 |
| #10590873 | 2 |
| #10589430 | 2 |
| C3×#4564 | 2 |
| #10589115 | 2 |
| #10589114 | 2 |
| Dic3×C3⋊C16 | 2 |
| #71318 | 3 |
| #69216 | 3 |