Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
385 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 385 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 |
|---|---|---|
| 1. C2×#63655 | C2 | semidirect |
| 2. C3×#5191 | C2 | semidirect |
| 3. #10590763 | C2 | semidirect |
| 5. C3×#4564 | C2 | semidirect |
| 6. Dic3⋊(C3⋊C16) | C2 | semidirect |
| 7. #10589114 | C2 | semidirect |
| 24. #5191 | D3 | semidirect |
| 33. #4564 | D3 | semidirect |
| 288. C32 | #2210 | semidirect |
| 334. C3 | #69235 | semidirect |
| 335. C3 | #71323 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63655 | 2 |
| C3×#5191 | 2 |
| #10590763 | 2 |
| C2×#63546 | 2 |
| C3×#4564 | 2 |
| Dic3⋊(C3⋊C16) | 2 |
| #10589114 | 2 |
| #71323 | 3 |
| #69235 | 3 |