Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
140 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 55 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 |
|---|---|---|
| 24. C32×C16 | Q8 | semidirect |
| 25. C3⋊(C3⋊C16) | Q8 | semidirect |
| 78. C16 | PSU(3,𝔽2) | semidirect |
| 82. C32 | #2183 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×PSU(3,𝔽2) | 2 |
| #10590135 | 2 |
| C16×#157 | 2 |
| #10590082 | 2 |
| #2183 | 9 |