Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
5928 conjugacy classes of subgroups; only the 1321 normal subgroups are shown.
This group has 5928 conjugacy classes of subgroups — too many to draw. Only its 1321 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×C4⋊(C3⋊D3) | C2 | semidirect |
| 2. C23×C32×C8 | C2 | semidirect |
| 3. C22×#3745 | C2 | direct (N × H) |
| 8. C22×C4⋊(C3⋊D3) | C22 | semidirect |
| 9. C22×C32×C8 | C22 | semidirect |
| 10. C2×#3745 | C22 | direct (N × H) |
| 12. C23×C3×C8 | D3 | semidirect |
| 20. C2×C4⋊(C3⋊D3) | C23 | semidirect |
| 21. C2×C32×C8 | C23 | semidirect |
| 22. #3745 | C23 | direct (N × H) |
| 28. C22×C3×C8 | C2×D3 | semidirect |
| 30. C23×C32 | D8 | semidirect |
| 37. C4⋊(C3⋊D3) | C24 | semidirect |
| 38. C32×C8 | C24 | semidirect |
| 41. C23×C8 | C3⋊D3 | semidirect |
| 49. C2×C3×C8 | C22×D3 | semidirect |
| 51. C22×C32 | C2×D8 | semidirect |
| 62. C22×C8 | C2×C3⋊D3 | semidirect |
| 63. C23×C3 | D24 | semidirect |
| 71. C3×C8 | C23×D3 | semidirect |
| 72. C2×C32 | C22×D8 | semidirect |
| 83. C2×C8 | C22×C3⋊D3 | semidirect |
| 84. C22×C3 | C2×D24 | semidirect |
| 90. C32 | C23×D8 | semidirect |
| 93. C23 | #3745 | direct (N × H) |
| 99. C8 | C23×C3⋊D3 | semidirect |
| 100. C2×C3 | C22×D24 | semidirect |
| 105. C22 | C2×#3745 | direct (N × H) |
| 109. C3 | C23×D24 | semidirect |
| 111. C2 | C22×#3745 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4⋊(C3⋊D3) | 2 |
| C23×C32×C8 | 2 |
| C22×#3745 | 2 |
| C23×D24 | 3 |