Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
743 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 743 conjugacy classes of subgroups — too many to draw. Only its 142 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. C3×#5748 | C2 | semidirect |
| 2. C3×#5129 | C2 | semidirect |
| 3. C32×#338 | C2 | semidirect |
| 5. #68727 | C3 | direct (N × H) |
| 14. #5748 | C2×C3 | semidirect |
| 16. #5129 | C2×C3 | semidirect |
| 18. C3×#338 | D3 | semidirect |
| 19. C3×#338 | C2×C3 | semidirect |
| 63. #338 | C3×D3 | semidirect |
| 169. C32 | #2017 | semidirect |
| 198. C3 | #68727 | direct (N × H) |
| 199. C3 | C3×#2017 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5748 | 2 |
| C3×#5129 | 2 |
| C32×#338 | 2 |
| C3×#2017 | 3 |
| #68727 | 3 |