Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
296 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 20. #824 | C4 | direct (N × H) |
| 122. C3×C4 | #101 | semidirect |
| 162. C4 | #824 | direct (N × H) |
| 165. C3 | C4×#101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic6 | 2 |
| C3×C4×M16 | 2 |
| C2×#824 | 2 |
| C4×#208 | 2 |
| #4554 | 2 |
| C4×#101 | 3 |