Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
457 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 457 conjugacy classes of subgroups — too many to draw. Only its 114 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. C3×C8×Dic6 | C2 | semidirect |
| 4. C3×#4544 | C2 | semidirect |
| 5. C3×#4458 | C2 | semidirect |
| 7. #71286 | C3 | direct (N × H) |
| 24. #5075 | C2×C3 | semidirect |
| 25. C8×Dic6 | C2×C3 | semidirect |
| 28. #4544 | C2×C3 | semidirect |
| 29. #4458 | C2×C3 | semidirect |
| 84. C3×Dic6 | D8 | semidirect |
| 86. C32×C8 | SD16 | semidirect |
| 188. Dic6 | C3×D8 | semidirect |
| 195. C3×C8 | #214 | semidirect |
| 196. C3×C8 | C3×SD16 | semidirect |
| 249. C32 | #1668 | semidirect |
| 266. C8 | C3×#214 | semidirect |
| 291. C3 | #71286 | direct (N × H) |
| 292. C3 | C3×#1668 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#493 | 2 |
| C3×#5075 | 2 |
| C3×C8×Dic6 | 2 |
| C3×#4544 | 2 |
| C3×#4458 | 2 |
| C3×#1668 | 3 |
| #71286 | 3 |