Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
384 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 141 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. #4797 | C2 | direct (N × H) |
| 179. C2×C3 | #491 | semidirect |
| 196. C3 | C2×#491 | semidirect |
| 197. C2 | #4797 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#944 | 2 |
| C2×#890 | 2 |
| C2×C3×#103 | 2 |
| C2×#835 | 2 |
| C2×#816 | 2 |
| C2×#815 | 2 |
| C2×#810 | 2 |
| #4797 | 2 |
| C2×#491 | 3 |