Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
246 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 5. C2×C3×M16 | C4 | semidirect |
| 9. C3⋊#95 | C4 | semidirect |
| 24. C2×M16 | Dic3 | semidirect |
| 96. C3 | #1297 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#407 | 2 |
| C4×#217 | 2 |
| #1297 | 3 |