Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
390 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 390 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. C22×#208 | C2 | semidirect |
| 3. C3×#407 | C2 | semidirect |
| 4. C2×#823 | C2 | semidirect |
| 5. #4554 | C2 | semidirect |
| 27. #407 | D3 | semidirect |
| 56. #208 | D4 | semidirect |
| 146. C22×C3 | #100 | semidirect |
| 210. C22 | #823 | semidirect |
| 219. C3 | #1900 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#930 | 2 |
| C22×#208 | 2 |
| C3×#407 | 2 |
| C2×#823 | 2 |
| #4554 | 2 |
| #1900 | 3 |