Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
148 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 16. #829 | C4 | semidirect |
| 123. C3 | #2176 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×Q16 | 2 |
| C2×#829 | 2 |
| C4×Dic12 | 2 |
| #4564 | 2 |
| #4492 | 2 |
| #4490 | 2 |
| #4461 | 2 |
| #2176 | 3 |