Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
336 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 43. #216 | Q8 | direct (N × H) |
| 68. C3×Q8 | Q16 | semidirect |
| 114. Q8 | #216 | direct (N × H) |
| 137. C3 | Q8×Q16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Q82 | 2 |
| Q8×Dic6 | 2 |
| #5091 | 2 |
| #5078 | 2 |
| C4×#216 | 2 |
| Q8×C3⋊C8 | 2 |
| #5021 | 2 |
| Q8×Q16 | 3 |