Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
270 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 48 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. D8×#157 | C2 | semidirect |
| 3. #10590193 | C2 | semidirect |
| 4. #10590139 | C2 | semidirect |
| 5. #10590135 | C2 | semidirect |
| 12. C32×D16 | C4 | semidirect |
| 13. #63653 | C4 | semidirect |
| 14. #63626 | C4 | semidirect |
| 23. C32×D8 | C2×C4 | semidirect |
| 25. #3745 | C2×C4 | semidirect |
| 28. C32×C16 | C2×C4 | semidirect |
| 29. C3⋊(C3⋊C16) | C2×C4 | semidirect |
| 72. D16 | #157 | semidirect |
| 93. D8 | C2×#157 | semidirect |
| 101. C16 | C2×#157 | semidirect |
| 109. C32 | #2177 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×#157 | 2 |
| C3⋊D3×D16 | 2 |
| #10590193 | 2 |
| #10590139 | 2 |
| #10590135 | 2 |
| #2177 | 9 |