Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
298 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 106 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 |
|---|---|---|
| 4. #10590135 | C2 | direct (N × H) |
| 8. C2×#3708 | C4 | semidirect |
| 11. #63764 | C4 | semidirect |
| 13. C2×C32×C16 | C4 | semidirect |
| 14. C2×C3⋊(C3⋊C16) | C4 | semidirect |
| 15. C16×C3⋊D3 | C4 | semidirect |
| 31. #3708 | C2×C4 | semidirect |
| 32. C32×C16 | C2×C4 | semidirect |
| 33. C3⋊(C3⋊C16) | C2×C4 | semidirect |
| 85. C2×C16 | #157 | semidirect |
| 99. C2×C32 | #346 | semidirect |
| 101. C3⋊D3 | #346 | semidirect |
| 118. C16 | C2×#157 | semidirect |
| 127. C32 | C2×#346 | semidirect |
| 158. C2 | #10590135 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×#157 | 2 |
| C2×#63764 | 2 |
| C2×C16×C3⋊D3 | 2 |
| #10590135 | 2 |
| C2×#346 | 9 |