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 |
|---|---|---|
| 1. C32×C4×D8 | C2 | semidirect |
| 3. C4×#3745 | C2 | semidirect |
| 4. #10589428 | C2 | semidirect |
| 5. #10589357 | C2 | semidirect |
| 6. #10589355 | C2 | semidirect |
| 7. C4×C3⋊(C3⋊C16) | C2 | semidirect |
| 16. #63653 | C4 | direct (N × H) |
| 21. C3×C4×D8 | D3 | semidirect |
| 33. C32×D8 | C2×C4 | semidirect |
| 42. #3745 | C2×C4 | semidirect |
| 44. C3⋊(C3⋊C16) | C2×C4 | semidirect |
| 76. C4×D8 | C3⋊D3 | semidirect |
| 86. C3×D8 | C4×D3 | semidirect |
| 107. C32×C4 | D16 | semidirect |
| 151. D8 | C4×C3⋊D3 | semidirect |
| 170. C3×C4 | #826 | semidirect |
| 174. C32 | C4×D16 | semidirect |
| 206. C4 | #63653 | direct (N × H) |
| 209. C3 | C4×#826 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C4×D8 | 2 |
| C2×#63653 | 2 |
| C4×#3745 | 2 |
| #10589428 | 2 |
| #10589357 | 2 |
| #10589355 | 2 |
| C4×C3⋊(C3⋊C16) | 2 |
| C4×#826 | 3 |