Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
928 conjugacy classes of subgroups; only the 365 normal subgroups are shown.
This group has 928 conjugacy classes of subgroups — too many to draw. Only its 365 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. #4973 | C2 | direct (N × H) |
| 13. C22×Dic6 | C4 | semidirect |
| 38. C22×Dic3 | Q8 | semidirect |
| 44. C2×Dic6 | C2×C4 | semidirect |
| 80. C2×Dic3 | C2×Q8 | semidirect |
| 140. C2×C3 | #391 | semidirect |
| 160. C3 | C2×#391 | semidirect |
| 161. C2 | #4973 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic6 | 2 |
| C22×C3×C4⋊C4 | 2 |
| C22×C4×Dic3 | 2 |
| C2×C3⋊#95 | 2 |
| #4973 | 2 |
| C2×#391 | 3 |