Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
924 conjugacy classes of subgroups; only the 381 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 381 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. C22×C3×C42 | C2 | semidirect |
| 3. C2×C42×D3 | C2 | semidirect |
| 4. C4×#217 | C2 | semidirect |
| 5. C4×(C2×D3)⋊C4 | C2 | semidirect |
| 6. C4×Dic3⋊C4 | C2 | semidirect |
| 7. C42×Dic3 | C2 | semidirect |
| 16. C4×#67 | C4 | direct (N × H) |
| 26. C22×C42 | D3 | semidirect |
| 35. C22×C3×C4 | C2×C4 | semidirect |
| 44. C2×C4×D3 | C2×C4 | semidirect |
| 46. C3×C42 | D4 | semidirect |
| 47. #217 | C2×C4 | semidirect |
| 48. (C2×D3)⋊C4 | C2×C4 | semidirect |
| 49. Dic3⋊C4 | C2×C4 | semidirect |
| 52. C4×Dic3 | C2×C4 | semidirect |
| 82. #67 | C42 | direct (N × H) |
| 101. C22×C4 | C4×D3 | semidirect |
| 111. C42 | #67 | direct (N × H) |
| 114. C22×C3 | C2×C42 | semidirect |
| 120. C2×D3 | C2×C42 | semidirect |
| 122. C3×C4 | C4×D4 | semidirect |
| 125. Dic3 | C2×C42 | semidirect |
| 158. C22 | C42×D3 | semidirect |
| 166. C4 | C4×#67 | direct (N × H) |
| 167. C3 | C42×D4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C42 | 2 |
| C2×C4×#67 | 2 |
| C2×C42×D3 | 2 |
| C4×#217 | 2 |
| C4×(C2×D3)⋊C4 | 2 |
| C4×Dic3⋊C4 | 2 |
| C42×Dic3 | 2 |
| C42×D4 | 3 |