Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
424 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 197 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 |
|---|---|---|
| 3. #5080 | C2 | direct (N × H) |
| 43. C2×C3⋊C8 | Q8 | semidirect |
| 73. C3⋊C8 | C2×Q8 | semidirect |
| 118. C2×C3 | #498 | semidirect |
| 132. C3 | C2×#498 | semidirect |
| 133. C2 | #5080 | 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 |
| C2×#869 | 2 |
| #5080 | 2 |
| C2×#808 | 2 |
| C2×C4×C3⋊C8 | 2 |
| C2×#498 | 3 |