Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
442 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 87 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. C2×C42×D3 | C2 | semidirect |
| 3. C2×C3×#104 | C2 | semidirect |
| 4. C2×#837 | C2 | semidirect |
| 5. #5126 | C2 | semidirect |
| 6. #4555 | C2 | semidirect |
| 7. #4523 | C2 | semidirect |
| 14. #946 | C4 | semidirect |
| 15. #938 | C4 | semidirect |
| 31. C2×#104 | D3 | semidirect |
| 40. C2×C3×Q8 | C2×C4 | semidirect |
| 42. C2×C3×D4 | C2×C4 | semidirect |
| 61. C3×C42 | D4 | semidirect |
| 65. C4⋊Dic3 | C2×C4 | semidirect |
| 70. C4×Dic3 | D4 | semidirect |
| 135. C2×Q8 | C4×D3 | semidirect |
| 138. C2×D4 | C4×D3 | semidirect |
| 168. C42 | #67 | semidirect |
| 179. C2×D3 | #104 | semidirect |
| 252. C3 | #1896 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5828 | 2 |
| C2×C42×D3 | 2 |
| C2×C3×#104 | 2 |
| C2×#837 | 2 |
| #5126 | 2 |
| #4555 | 2 |
| #4523 | 2 |
| #1896 | 3 |