Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2952 conjugacy classes of subgroups; only the 814 normal subgroups are shown.
This group has 2952 conjugacy classes of subgroups — too many to draw. Only its 814 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. C24×C4×C9 | C2 | semidirect |
| 3. C22×#3676 | C2 | semidirect |
| 4. C2×#63491 | C2 | direct (N × H) |
| 5. C22×(C2×D9)⋊C4 | C2 | semidirect |
| 6. C22×Dic9⋊C4 | C2 | semidirect |
| 12. C23×C4×C9 | C22 | semidirect |
| 17. C2×#3676 | C22 | semidirect |
| 18. #63491 | C22 | direct (N × H) |
| 19. C2×(C2×D9)⋊C4 | C22 | semidirect |
| 20. C2×Dic9⋊C4 | C22 | semidirect |
| 37. C22×C4×C9 | C23 | semidirect |
| 44. #3676 | C23 | semidirect |
| 45. (C2×D9)⋊C4 | C23 | semidirect |
| 46. Dic9⋊C4 | C23 | semidirect |
| 81. C24×C4 | D9 | semidirect |
| 108. C22×C9 | #123 | semidirect |
| 127. C23×C4 | C2×D9 | semidirect |
| 152. C2×C9 | C2×#123 | semidirect |
| 172. C22×C4 | C22×D9 | semidirect |
| 189. C9 | C22×#123 | semidirect |
| 219. C22 | #63491 | direct (N × H) |
| 230. C2 | C2×#63491 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C4×C9 | 2 |
| C23×#611 | 2 |
| C22×#3676 | 2 |
| C2×#63491 | 2 |
| C22×(C2×D9)⋊C4 | 2 |
| C22×Dic9⋊C4 | 2 |
| C22×#929 | 3 |