Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
389 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 389 conjugacy classes of subgroups — too many to draw. Only its 78 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×#5155 | C2 | semidirect |
| 3. #10590763 | C2 | semidirect |
| 4. C2×#63549 | C2 | semidirect |
| 5. C3×#4562 | C2 | semidirect |
| 6. Dic3⋊(C3⋊C16) | C2 | semidirect |
| 7. #10589117 | C2 | semidirect |
| 25. #5155 | D3 | semidirect |
| 34. #4562 | D3 | semidirect |
| 290. C32 | #2210 | semidirect |
| 337. C3 | #69203 | semidirect |
| 338. C3 | #71323 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63653 | 2 |
| C3×#5155 | 2 |
| #10590763 | 2 |
| C2×#63549 | 2 |
| C3×#4562 | 2 |
| Dic3⋊(C3⋊C16) | 2 |
| #10589117 | 2 |
| #71323 | 3 |
| #69203 | 3 |