Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
166 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
| 6. C22×C3×C8 | C4 | semidirect |
| 10. #834 | C4 | semidirect |
| 28. C2×M16 | Dic3 | semidirect |
| 29. C22×C8 | Dic3 | semidirect |
| 102. C3 | #1391 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#408 | 2 |
| #5240 | 2 |
| #1391 | 3 |