Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
438 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 103 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×C4×D12 | C2 | semidirect |
| 3. C3×#390 | C2 | semidirect |
| 4. C2×#832 | C2 | semidirect |
| 5. C2×#809 | C2 | semidirect |
| 6. #4529 | C2 | semidirect |
| 7. #4524 | C2 | semidirect |
| 18. C2×#213 | C4 | semidirect |
| 31. #390 | D3 | semidirect |
| 41. C2×C3×D4 | C2×C4 | semidirect |
| 71. C2×C3⋊C8 | C2×C4 | semidirect |
| 117. C2×C3×C4 | D8 | semidirect |
| 130. D12 | C22⋊C4 | semidirect |
| 147. C2×D4 | C4×D3 | semidirect |
| 236. C2×C4 | #213 | semidirect |
| 283. C3 | #1879 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#213 | 2 |
| C2×C4×D12 | 2 |
| C3×#390 | 2 |
| C2×#832 | 2 |
| C2×#809 | 2 |
| #4529 | 2 |
| #4524 | 2 |
| #1879 | 3 |