Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
164 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 23. C3×Q16 | C8 | semidirect |
| 56. C3⋊C8 | Q16 | direct (N × H) |
| 58. Q16 | C3⋊C8 | direct (N × H) |
| 101. C3 | C8×Q16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×Q16 | 2 |
| Q8×C3⋊C8 | 2 |
| #4535 | 2 |
| #4458 | 2 |
| C8×C3⋊C8 | 2 |
| C8×Q16 | 3 |