Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
390 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 1. C22×C3×Q16 | C2 | semidirect |
| 4. #5229 | C2 | semidirect |
| 5. C2×#835 | C2 | semidirect |
| 7. #4550 | C2 | semidirect |
| 28. C22×Q16 | D3 | semidirect |
| 244. C3 | #2015 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×Q16 | 2 |
| C2×#947 | 2 |
| C22×#215 | 2 |
| #5229 | 2 |
| C2×#835 | 2 |
| C2×#821 | 2 |
| #4550 | 2 |
| #2015 | 3 |