Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
324 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 97 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. #5121 | C2 | semidirect |
| 5. #4555 | C2 | semidirect |
| 16. C3×#100 | C4 | semidirect |
| 35. C3×M16 | C2×C4 | semidirect |
| 56. #100 | Dic3 | semidirect |
| 90. M16 | C2×Dic3 | semidirect |
| 160. C3 | #1856 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5798 | 2 |
| C2×C3×#100 | 2 |
| #5221 | 2 |
| #5121 | 2 |
| #4555 | 2 |
| #1856 | 3 |