Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
332 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 93 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. Dic3×#41 | C2 | semidirect |
| 3. #5240 | C2 | semidirect |
| 4. #5236 | C2 | semidirect |
| 5. C2×#837 | C2 | semidirect |
| 6. #4559 | C2 | semidirect |
| 7. #4555 | C2 | semidirect |
| 12. C3×#137 | C4 | semidirect |
| 14. C3×AGL(1,ℤ/8) | C4 | semidirect |
| 45. C2×C3×Q8 | C2×C4 | semidirect |
| 49. C2×C3×D4 | C2×C4 | semidirect |
| 61. C3×M16 | C2×C4 | semidirect |
| 81. #137 | Dic3 | semidirect |
| 83. AGL(1,ℤ/8) | Dic3 | semidirect |
| 142. C2×Q8 | C2×Dic3 | semidirect |
| 146. C2×D4 | C2×Dic3 | semidirect |
| 160. M16 | C2×Dic3 | semidirect |
| 252. C3 | #1906 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#575 | 2 |
| Dic3×#41 | 2 |
| #5240 | 2 |
| #5236 | 2 |
| C2×#837 | 2 |
| #4559 | 2 |
| #4555 | 2 |
| #1906 | 3 |