Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
522 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 157 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. C4×#3745 | C2 | semidirect |
| 3. C32×C4×C16 | C2 | semidirect |
| 4. #10589375 | C2 | semidirect |
| 5. #10589370 | C2 | semidirect |
| 14. #63626 | C4 | direct (N × H) |
| 17. C3×C4×C16 | D3 | semidirect |
| 28. #3745 | C2×C4 | semidirect |
| 30. C32×C16 | C2×C4 | semidirect |
| 55. C4×C16 | C3⋊D3 | semidirect |
| 66. C3×C16 | C4×D3 | semidirect |
| 72. C32×C4 | D16 | semidirect |
| 109. C16 | C4×C3⋊D3 | semidirect |
| 115. C3×C4 | D48 | semidirect |
| 119. C32 | C4×D16 | semidirect |
| 141. C4 | #63626 | direct (N × H) |
| 144. C3 | C4×D48 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63626 | 2 |
| C4×#3745 | 2 |
| C32×C4×C16 | 2 |
| #10589375 | 2 |
| #10589370 | 2 |
| C4×D48 | 3 |