Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
172 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 22. C3×M16 | C8 | semidirect |
| 59. M16 | C3⋊C8 | semidirect |
| 108. C3 | #1278 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×M16 | 2 |
| #4925 | 2 |
| C2×C4×C3⋊C8 | 2 |
| #1278 | 3 |