Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
286 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 83 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. C3×#428 | C2 | semidirect |
| 4. #4977 | C2 | semidirect |
| 6. #4554 | C2 | semidirect |
| 7. #4532 | C2 | semidirect |
| 24. #825 | C4 | semidirect |
| 28. #428 | D3 | semidirect |
| 48. C3×M16 | C2×C4 | semidirect |
| 62. C4×Dic3 | C2×C4 | semidirect |
| 129. M16 | C4×D3 | semidirect |
| 216. C3 | #1860 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5523 | 2 |
| C3×#428 | 2 |
| C2×#825 | 2 |
| #4977 | 2 |
| #4966 | 2 |
| #4554 | 2 |
| #4532 | 2 |
| #1860 | 3 |