Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
324 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 8. C3×C4⋊Q8 | C4 | semidirect |
| 43. C4⋊Q8 | Dic3 | semidirect |
| 96. C3×C4 | #103 | semidirect |
| 133. C4 | #835 | semidirect |
| 137. C3 | #1981 | semidirect |
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×#835 | 2 |
| C4×C4⋊Dic3 | 2 |
| C2×C4⋊(C3⋊C8) | 2 |
| #1981 | 3 |