Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1126 conjugacy classes of subgroups; only the 463 normal subgroups are shown.
This group has 1126 conjugacy classes of subgroups — too many to draw. Only its 463 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 |
|---|---|---|
| 3. #10596547 | C2 | direct (N × H) |
| 27. C2×C32×Q8 | Q8 | semidirect |
| 28. Q8×C3⋊D3 | Q8 | semidirect |
| 31. C2×#634 | Q8 | semidirect |
| 51. C32×Q8 | C2×Q8 | semidirect |
| 56. #634 | C2×Q8 | semidirect |
| 100. C2×C32 | #557 | semidirect |
| 102. C3⋊D3 | #557 | semidirect |
| 110. C2×Q8 | PSU(3,𝔽2) | semidirect |
| 130. C32 | C2×#557 | semidirect |
| 134. Q8 | C2×PSU(3,𝔽2) | semidirect |
| 167. C2 | #10596547 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×#157 | 2 |
| #10596547 | 2 |
| C2×C4⋊PSU(3,𝔽2) | 2 |
| C2×C4×PSU(3,𝔽2) | 2 |
| C2×#64243 | 2 |
| C2×#557 | 9 |