Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
390 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 390 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 |
|---|---|---|
| 1. C22×C3×M16 | C2 | semidirect |
| 3. #5207 | C2 | semidirect |
| 4. C2×#823 | C2 | semidirect |
| 5. #4554 | C2 | semidirect |
| 24. C22×M16 | D3 | semidirect |
| 49. C3×M16 | D4 | semidirect |
| 130. M16 | #67 | 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 |
|---|---|
| C22×C3×M16 | 2 |
| C2×#930 | 2 |
| #5207 | 2 |
| C2×#823 | 2 |
| #4554 | 2 |
| #1900 | 3 |