Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
449 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 449 conjugacy classes of subgroups — too many to draw. Only its 84 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×#5075 | C2 | semidirect |
| 3. #10590367 | C2 | semidirect |
| 4. #10590259 | C2 | semidirect |
| 5. C3×#4544 | C2 | semidirect |
| 6. #10589098 | C2 | semidirect |
| 7. #10589091 | C2 | semidirect |
| 26. #5075 | D3 | semidirect |
| 35. #4544 | D3 | semidirect |
| 116. C3⋊(C3⋊C8) | SD16 | semidirect |
| 337. C32 | #1688 | semidirect |
| 392. C3 | #68413 | semidirect |
| 393. C3 | #71025 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592772 | 2 |
| C3×#5075 | 2 |
| #10590367 | 2 |
| #10590259 | 2 |
| C3×#4544 | 2 |
| #10589098 | 2 |
| #10589091 | 2 |
| #71025 | 3 |
| #68413 | 3 |