Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
224 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 2. C2×C3×M32 | C2 | semidirect |
| 3. C22×C3⋊C16 | C2 | semidirect |
| 4. #4515 | C2 | direct (N × H) |
| 16. C3×M32 | C22 | semidirect |
| 20. C2×C3⋊C16 | C22 | semidirect |
| 22. C2×M32 | D3 | semidirect |
| 59. M32 | C2×D3 | semidirect |
| 145. C2×C3 | #350 | semidirect |
| 159. C3 | C2×#350 | semidirect |
| 163. C2 | #4515 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#901 | 2 |
| C2×C3×M32 | 2 |
| C22×C3⋊C16 | 2 |
| #4515 | 2 |
| C2×#350 | 3 |