Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
260 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 3. #5106 | C2 | semidirect |
| 4. #4557 | C2 | semidirect |
| 9. C2×C3×M16 | C4 | semidirect |
| 11. C22×C3×C8 | C4 | semidirect |
| 43. C2×M16 | Dic3 | semidirect |
| 45. C22×C8 | Dic3 | semidirect |
| 128. C3 | #1812 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#131 | 2 |
| #5240 | 2 |
| #5106 | 2 |
| #4557 | 2 |
| #1812 | 3 |