Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
336 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 132. Dic6 | Q16 | semidirect |
| 221. C3 | #3363 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5722 | 2 |
| #5567 | 2 |
| C3×#477 | 2 |
| #5093 | 2 |
| C4×#216 | 2 |
| #4875 | 2 |
| #4873 | 2 |
| #4849 | 2 |
| #4830 | 2 |
| #4795 | 2 |
| #4792 | 2 |
| #3363 | 3 |