Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
462 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 143 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 |
|---|---|---|
| 5. #10593536 | C2 | direct (N × H) |
| 23. C2×#622 | Q8 | semidirect |
| 28. #3787 | Q8 | semidirect |
| 31. C2×C32×C8 | Q8 | semidirect |
| 32. C2×C3⋊(C3⋊C8) | Q8 | semidirect |
| 33. C8×C3⋊D3 | Q8 | semidirect |
| 51. #622 | C2×Q8 | semidirect |
| 52. C32×C8 | C2×Q8 | semidirect |
| 53. C3⋊(C3⋊C8) | C2×Q8 | semidirect |
| 96. C2×C32 | #500 | semidirect |
| 98. C3⋊D3 | #500 | semidirect |
| 113. C2×C8 | PSU(3,𝔽2) | semidirect |
| 128. C32 | C2×#500 | semidirect |
| 145. C8 | C2×PSU(3,𝔽2) | semidirect |
| 167. C2 | #10593536 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊PSU(3,𝔽2) | 2 |
| C2×#63769 | 2 |
| C2×C8×#157 | 2 |
| C2×#63746 | 2 |
| #10593536 | 2 |
| C2×#500 | 9 |