Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
336 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 67. #216 | Q8 | semidirect |
| 131. Dic6 | Q16 | semidirect |
| 219. C3 | Q8×Q16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5722 | 2 |
| Q8×Dic6 | 2 |
| C3×#477 | 2 |
| #5078 | 2 |
| C4×#216 | 2 |
| #4875 | 2 |
| #4874 | 2 |
| #4850 | 2 |
| #4830 | 2 |
| #4793 | 2 |
| #4790 | 2 |
| Q8×Q16 | 3 |