Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
424 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 181 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. #4681 | C2 | direct (N × H) |
| 120. C2×C3 | #487 | semidirect |
| 134. C3 | C2×#487 | semidirect |
| 135. C2 | #4681 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#869 | 2 |
| C2×C3×C4×C8 | 2 |
| C2×#816 | 2 |
| #4681 | 2 |
| C2×#487 | 3 |