Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
521 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 521 conjugacy classes of subgroups — too many to draw. Only its 130 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×#5076 | C2 | semidirect |
| 3. C3×#5070 | C2 | semidirect |
| 4. C3×#4680 | C2 | semidirect |
| 5. C3×#4455 | C2 | semidirect |
| 7. #71277 | C3 | direct (N × H) |
| 23. #5076 | C2×C3 | semidirect |
| 24. #5070 | C2×C3 | semidirect |
| 25. #4680 | C2×C3 | semidirect |
| 27. #4455 | C2×C3 | semidirect |
| 73. C32×C8 | SD16 | semidirect |
| 158. C3×C8 | #214 | semidirect |
| 159. C3×C8 | C3×SD16 | semidirect |
| 200. C32 | #1715 | semidirect |
| 212. C8 | C3×#214 | semidirect |
| 234. C3 | #71277 | direct (N × H) |
| 235. C3 | C3×#1715 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#493 | 2 |
| C3×#5076 | 2 |
| C3×#5070 | 2 |
| C3×#4680 | 2 |
| C3×#4455 | 2 |
| C3×#1715 | 3 |
| #71277 | 3 |