Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1190 conjugacy classes of subgroups; only the 503 normal subgroups are shown.
This group has 1190 conjugacy classes of subgroups — too many to draw. Only its 503 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 |
|---|---|---|
| 2. Q8×PSU(3,𝔽2) | C2 | direct (N × H) |
| 17. C2×PSU(3,𝔽2) | Q8 | direct (N × H) |
| 20. C2×C32×Q8 | Q8 | semidirect |
| 21. Q8×C3⋊D3 | Q8 | semidirect |
| 24. C2×#634 | Q8 | semidirect |
| 36. PSU(3,𝔽2) | C2×Q8 | direct (N × H) |
| 37. C32×Q8 | C2×Q8 | semidirect |
| 42. #634 | C2×Q8 | semidirect |
| 77. C2×C32 | Q82 | semidirect |
| 79. C3⋊D3 | Q82 | semidirect |
| 89. C2×Q8 | PSU(3,𝔽2) | direct (N × H) |
| 103. C32 | C2×Q82 | semidirect |
| 108. Q8 | C2×PSU(3,𝔽2) | direct (N × H) |
| 135. C2 | Q8×PSU(3,𝔽2) | 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 |
| Q8×PSU(3,𝔽2) | 2 |
| C2×C4⋊PSU(3,𝔽2) | 2 |
| C2×C4×PSU(3,𝔽2) | 2 |
| C2×Q82 | 9 |