Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
687 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 687 conjugacy classes of subgroups — too many to draw. Only its 107 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. #5819⋊C3 | C2 | semidirect |
| 4. #5750⋊C3 | C2 | semidirect |
| 5. D3×#131⋊C3 | C2 | semidirect |
| 6. #87160 | C3 | semidirect |
| 14. C3×#131⋊C3 | C22 | semidirect |
| 15. C3×#131⋊C3 | C22 | semidirect |
| 16. C3⋊(#131⋊C3) | C22 | semidirect |
| 19. C2×C3×#131 | C2×C3 | semidirect |
| 20. #5819 | C2×C3 | semidirect |
| 22. #5750 | C2×C3 | semidirect |
| 24. D3×#131 | C2×C3 | semidirect |
| 33. C2×#131⋊C3 | D3 | semidirect |
| 95. #131⋊C3 | C2×D3 | semidirect |
| 96. #131⋊C3 | C2×D3 | semidirect |
| 116. C2×#131 | C3×D3 | semidirect |
| 440. C3 | #85629 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5964⋊C3 | 2 |
| C2×C3×#131⋊C3 | 2 |
| #5819⋊C3 | 2 |
| #5750⋊C3 | 2 |
| D3×#131⋊C3 | 2 |
| #87160 | 3 |
| #85629 | 3 |
| C3×#901 | 4 |