Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2580 conjugacy classes of subgroups; only the 814 normal subgroups are shown.
This group has 2580 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. C23×Q8×C9 | C2 | semidirect |
| 3. C22×#3675 | C2 | direct (N × H) |
| 4. C23×C9⋊C8 | C2 | semidirect |
| 8. C22×Q8×C9 | C22 | semidirect |
| 13. C2×#3675 | C22 | direct (N × H) |
| 14. C22×C9⋊C8 | C22 | semidirect |
| 23. C2×Q8×C9 | C23 | semidirect |
| 29. #3675 | C23 | direct (N × H) |
| 30. C2×C9⋊C8 | C23 | semidirect |
| 41. C23×C9 | SD16 | semidirect |
| 46. Q8×C9 | C24 | semidirect |
| 52. C9⋊C8 | C24 | semidirect |
| 53. C23×Q8 | D9 | semidirect |
| 69. C22×C9 | C2×SD16 | semidirect |
| 78. C22×Q8 | C2×D9 | semidirect |
| 97. C2×C9 | C22×SD16 | semidirect |
| 104. C2×Q8 | C22×D9 | semidirect |
| 119. C9 | C23×SD16 | semidirect |
| 122. C23 | #3675 | direct (N × H) |
| 125. Q8 | C23×D9 | semidirect |
| 137. C22 | C2×#3675 | direct (N × H) |
| 144. C2 | C22×#3675 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Q8×C9 | 2 |
| C23×D36 | 2 |
| C22×#3675 | 2 |
| C23×C9⋊C8 | 2 |
| C23×#215 | 3 |