Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
480 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 183 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 |
|---|---|---|
| 3. C3×#441 | C2 | semidirect |
| 4. #5184 | C2 | semidirect |
| 5. #5030 | C2 | semidirect |
| 7. #4853 | C2 | semidirect |
| 9. #4789 | C2 | semidirect |
| 10. #4716 | C2 | semidirect |
| 18. D3×Q16 | C4 | semidirect |
| 48. #441 | D3 | direct (N × H) |
| 61. C3×Q16 | C2×C4 | semidirect |
| 68. #216 | C2×C4 | semidirect |
| 81. Dic12 | C2×C4 | semidirect |
| 146. Q16 | C4×D3 | semidirect |
| 204. D3 | #441 | direct (N × H) |
| 217. C3 | C2×#441 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×Q16 | 2 |
| C4×D3×Q8 | 2 |
| C3×#441 | 2 |
| #5184 | 2 |
| #5030 | 2 |
| D3×#106 | 2 |
| #4853 | 2 |
| D3×#103 | 2 |
| #4789 | 2 |
| #4716 | 2 |
| D3×#97 | 2 |
| C2×#441 | 3 |