Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×C3×AGL(1,ℤ/8) | C2 | semidirect |
| 2. #5825 | C2 | semidirect |
| 3. C2×#950 | C2 | semidirect |
| 4. #5805 | C2 | semidirect |
| 5. C22×#214 | C2 | semidirect |
| 6. C2×#909 | C2 | semidirect |
| 7. #5175 | C2 | semidirect |
| 8. #5167 | C2 | semidirect |
| 9. #5155 | C2 | semidirect |
| 10. #5154 | C2 | semidirect |
| 11. #5122 | C2 | semidirect |
| 23. #944 | C22 | semidirect |
| 24. C2×#216 | C22 | semidirect |
| 25. C2×#215 | C22 | semidirect |
| 29. #936 | C22 | semidirect |
| 34. C2×#214 | C22 | semidirect |
| 35. C2×#213 | C22 | semidirect |
| 40. C2×Dic12 | C22 | semidirect |
| 41. C2×#204 | C22 | semidirect |
| 42. #815 | C22 | semidirect |
| 43. C8×Dic3 | C22 | semidirect |
| 45. C2×AGL(1,ℤ/8) | D3 | semidirect |
| 81. C3×M16 | D4 | semidirect |
| 95. C2×C3⋊C8 | D4 | semidirect |
| 202. M16 | #67 | semidirect |
| 290. C3 | #3154 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×AGL(1,ℤ/8) | 2 |
| #5825 | 2 |
| C2×#950 | 2 |
| #5805 | 2 |
| C22×#214 | 2 |
| C2×#909 | 2 |
| #5175 | 2 |
| #5167 | 2 |
| #5155 | 2 |
| #5154 | 2 |
| #5122 | 2 |
| #3154 | 3 |