Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
856 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 856 conjugacy classes of subgroups — too many to draw. Only its 309 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. C22×C4×Dic3 | C2 | semidirect |
| 3. C22×#208 | C2 | semidirect |
| 4. C2×#837 | C2 | direct (N × H) |
| 8. C2×C3×#41 | C4 | semidirect |
| 10. C22×C3×Q8 | C4 | semidirect |
| 12. C22×C3×D4 | C4 | semidirect |
| 17. C2×C4×Dic3 | C22 | semidirect |
| 19. C2×#208 | C22 | semidirect |
| 21. #837 | C22 | direct (N × H) |
| 31. C3×#41 | C2×C4 | semidirect |
| 34. C2×C3×Q8 | C2×C4 | semidirect |
| 38. C2×C3×D4 | C2×C4 | semidirect |
| 51. C4×Dic3 | C23 | semidirect |
| 53. #208 | C23 | semidirect |
| 57. C2×#41 | Dic3 | semidirect |
| 59. C22×Q8 | Dic3 | semidirect |
| 61. C22×D4 | Dic3 | semidirect |
| 78. C3×Q8 | C22×C4 | semidirect |
| 82. C3×D4 | C22×C4 | semidirect |
| 103. #41 | C2×Dic3 | semidirect |
| 106. C2×Q8 | C2×Dic3 | semidirect |
| 110. C2×D4 | C2×Dic3 | semidirect |
| 131. C22×C3 | #104 | semidirect |
| 148. Q8 | C22×Dic3 | semidirect |
| 152. D4 | C22×Dic3 | semidirect |
| 171. C2×C3 | C2×#104 | semidirect |
| 177. C22 | #837 | direct (N × H) |
| 187. C3 | C22×#104 | semidirect |
| 191. C2 | C2×#837 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×#41 | 2 |
| C22×C4×Dic3 | 2 |
| C22×#208 | 2 |
| C2×#837 | 2 |
| C22×#104 | 3 |