Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
709 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 709 conjugacy classes of subgroups — too many to draw. Only its 111 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×#131⋊C3 | C2 | semidirect |
| 3. C2×C3⋊(#131⋊C3) | C2 | semidirect |
| 4. #5750⋊C3 | C2 | direct (N × H) |
| 5. C2×#5750 | C3 | semidirect |
| 13. C3×#131⋊C3 | C22 | semidirect |
| 14. C3⋊(#131⋊C3) | C22 | semidirect |
| 17. C2×C3×#131 | C2×C3 | semidirect |
| 18. C2×#948 | C2×C3 | semidirect |
| 20. #5750 | C2×C3 | semidirect |
| 28. C2×#131⋊C3 | D3 | semidirect |
| 57. C3×#131 | C22×C3 | semidirect |
| 62. #948 | C22×C3 | semidirect |
| 80. #131⋊C3 | C2×D3 | semidirect |
| 95. C2×#131 | C3×D3 | semidirect |
| 186. #131 | C2×C3×D3 | semidirect |
| 376. C2×C3 | #568⋊C3 | semidirect |
| 398. C3 | C2×#568⋊C3 | semidirect |
| 403. C2 | #5750⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×#41⋊C3 | 2 |
| C2×C3×#131⋊C3 | 2 |
| C2×C3⋊(#131⋊C3) | 2 |
| #5750⋊C3 | 2 |
| C2×#5750 | 3 |
| C2×#568⋊C3 | 3 |
| C2×C3×ΓL(1,𝔽25) | 4 |