Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
206 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 74. C3×Q8 | Q16 | semidirect |
| 88. Dic6 | Q16 | semidirect |
| 133. Q8 | Dic12 | semidirect |
| 161. C3 | #1633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic6 | 2 |
| #5021 | 2 |
| #4850 | 2 |
| #4699 | 2 |
| C3×Q8⋊C8 | 2 |
| #4481 | 2 |
| #4456 | 2 |
| #1633 | 3 |