Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
377 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 377 conjugacy classes of subgroups — too many to draw. Only its 82 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×#5183 | C2 | semidirect |
| 5. C3×#4564 | C2 | semidirect |
| 6. Dic3⋊(C3⋊C16) | C2 | semidirect |
| 7. #10589117 | C2 | semidirect |
| 24. #5183 | D3 | semidirect |
| 34. #4564 | D3 | semidirect |
| 171. C3×Dic3 | SD32 | semidirect |
| 280. Dic3 | #828 | semidirect |
| 281. C32 | #2208 | semidirect |
| 323. C3 | #69234 | semidirect |
| 324. C3 | #71315 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63655 | 2 |
| C3×#5183 | 2 |
| #10590763 | 2 |
| C2×#63549 | 2 |
| C3×#4564 | 2 |
| Dic3⋊(C3⋊C16) | 2 |
| #10589117 | 2 |
| #71315 | 3 |
| #69234 | 3 |