Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
456 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 189 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 |
|---|---|---|
| 81. C3⋊(C3⋊C8) | Q16 | semidirect |
| 179. C32 | #1584 | semidirect |
| 211. C3 | #70903 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C4×Q16 | 2 |
| #10592723 | 2 |
| Q8×C3⋊(C3⋊C8) | 2 |
| #10589401 | 2 |
| #10589324 | 2 |
| #10589320 | 2 |
| #70903 | 3 |