Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
336 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 95 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. #5118 | C2 | semidirect |
| 5. #4554 | C2 | semidirect |
| 120. Dic3 | #100 | semidirect |
| 166. C3 | #1800 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×Dic3 | 2 |
| C2×C3×#100 | 2 |
| C2×#833 | 2 |
| #5118 | 2 |
| #4554 | 2 |
| #1800 | 3 |