Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
480 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 173 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 |
|---|---|---|
| 6. #4849 | C2 | direct (N × H) |
| 75. C2×C3×C4 | Q16 | semidirect |
| 126. C3×C4 | C2×Q16 | semidirect |
| 146. C2×C4 | Dic12 | semidirect |
| 154. C2×C3 | #462 | semidirect |
| 167. C4 | C2×Dic12 | semidirect |
| 170. C3 | C2×#462 | semidirect |
| 171. C2 | #4849 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic12 | 2 |
| C2×#869 | 2 |
| C2×C4×Dic6 | 2 |
| C2×C3×C4⋊C8 | 2 |
| C2×#816 | 2 |
| #4849 | 2 |
| C2×#462 | 3 |