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 |
|---|---|---|
| 4. #5121 | C2 | semidirect |
| 5. #4977 | C2 | semidirect |
| 6. C3×#343 | C2 | semidirect |
| 7. #4555 | C2 | semidirect |
| 22. #825 | C4 | semidirect |
| 32. #343 | D3 | semidirect |
| 50. C3×M16 | C2×C4 | semidirect |
| 65. 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 |
|---|---|
| #5504 | 2 |
| C2×#825 | 2 |
| #5133 | 2 |
| #5121 | 2 |
| #4977 | 2 |
| C3×#343 | 2 |
| #4555 | 2 |
| #1860 | 3 |