Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
386 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 4. #4943 | C2 | semidirect |
| 5. #4527 | C2 | semidirect |
| 15. #935 | C4 | semidirect |
| 40. C22×Dic3 | C2×C4 | semidirect |
| 49. #217 | C2×C4 | semidirect |
| 193. C3 | #1890 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5798 | 2 |
| C2×#935 | 2 |
| C2×C3×#99 | 2 |
| #4943 | 2 |
| #4527 | 2 |
| #1890 | 3 |