Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
282 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 34. C2×C3×C8 | Q8 | semidirect |
| 41. C4⋊Dic3 | Q8 | semidirect |
| 87. C2×C8 | Dic6 | semidirect |
| 153. C3 | #2058 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#869 | 2 |
| C2×#817 | 2 |
| #4928 | 2 |
| C3×#336 | 2 |
| #4551 | 2 |
| #2058 | 3 |