Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
360 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 4. #5004 | C2 | semidirect |
| 5. #4532 | C2 | semidirect |
| 14. #936 | C4 | semidirect |
| 36. C2×Dic6 | C2×C4 | semidirect |
| 43. C4×Dic3 | C2×C4 | semidirect |
| 155. C3 | #1885 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#518 | 2 |
| C2×#936 | 2 |
| C2×#833 | 2 |
| #5004 | 2 |
| #4532 | 2 |
| #1885 | 3 |