Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
422 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 159 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. #10593532 | C2 | semidirect |
| 5. C8×PSU(3,𝔽2) | C2 | semidirect |
| 35. C32×M16 | Q8 | semidirect |
| 36. #3748 | Q8 | semidirect |
| 37. #3743 | Q8 | semidirect |
| 49. PSU(3,𝔽2) | M16 | direct (N × H) |
| 57. C32×C8 | C2×Q8 | semidirect |
| 58. C3⋊(C3⋊C8) | C2×Q8 | semidirect |
| 119. M16 | PSU(3,𝔽2) | direct (N × H) |
| 138. C32 | Q8×M16 | semidirect |
| 156. C8 | C2×PSU(3,𝔽2) | semidirect |
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 |
| M16×#157 | 2 |
| #10593539 | 2 |
| #10593532 | 2 |
| C8×PSU(3,𝔽2) | 2 |
| Q8×M16 | 9 |