Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
345 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 345 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. C2×C3×#829 | C2 | semidirect |
| 3. Dic3×Dic12 | C2 | semidirect |
| 5. #10589430 | C2 | semidirect |
| 6. Dic3⋊(C3⋊C16) | C2 | semidirect |
| 27. C2×#829 | D3 | semidirect |
| 271. C32 | #2211 | semidirect |
| 311. C3 | #71324 | semidirect |
| 312. C3 | #71498 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5191 | 2 |
| C2×C3×#829 | 2 |
| Dic3×Dic12 | 2 |
| C2×#63547 | 2 |
| #10589430 | 2 |
| Dic3⋊(C3⋊C16) | 2 |
| #10589115 | 2 |
| #71498 | 3 |
| #71324 | 3 |