Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
340 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 89 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. C3×#568 | C2 | semidirect |
| 3. #5237 | C2 | semidirect |
| 4. C2×#823 | C2 | semidirect |
| 5. #4559 | C2 | semidirect |
| 21. #568 | D3 | semidirect |
| 41. C3×M16 | D4 | semidirect |
| 104. M16 | #67 | semidirect |
| 165. C3 | #1914 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#568 | 2 |
| #5830 | 2 |
| #5237 | 2 |
| C2×#823 | 2 |
| #4559 | 2 |
| #1914 | 3 |