Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
292 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 40. C2×Dic6 | C8 | semidirect |
| 46. C2×C3×C8 | Q8 | semidirect |
| 61. C2×C3⋊C8 | Q8 | semidirect |
| 128. C2×C8 | Dic6 | semidirect |
| 209. C3 | #1984 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic6 | 2 |
| C2×Dic3⋊C8 | 2 |
| C2×C8×Dic3 | 2 |
| C3×#336 | 2 |
| #4550 | 2 |
| #4524 | 2 |
| #1984 | 3 |