Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
488 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 221 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 |
|---|---|---|
| 5. C4×#216 | C2 | direct (N × H) |
| 18. C2×#216 | C4 | direct (N × H) |
| 60. #216 | C2×C4 | direct (N × H) |
| 99. C2×C3×C4 | Q16 | semidirect |
| 153. C3×C4 | C2×Q16 | semidirect |
| 174. C2×C4 | #216 | direct (N × H) |
| 183. C2×C3 | C4×Q16 | semidirect |
| 197. C4 | C2×#216 | direct (N × H) |
| 200. C3 | C2×C4×Q16 | semidirect |
| 201. C2 | C4×#216 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×Q8 | 2 |
| C22×#216 | 2 |
| C2×C4×Dic6 | 2 |
| C2×#835 | 2 |
| C4×#216 | 2 |
| C2×#810 | 2 |
| C2×#807 | 2 |
| C2×C4×C3⋊C8 | 2 |
| C2×C4×Q16 | 3 |