Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
460 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 213 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 |
|---|---|---|
| 3. C2×C3×#108 | C2 | semidirect |
| 4. C2×#822 | C2 | semidirect |
| 5. C2×#819 | C2 | semidirect |
| 6. #4893 | C2 | direct (N × H) |
| 20. C3×#108 | C22 | semidirect |
| 21. #822 | C22 | semidirect |
| 22. #819 | C22 | semidirect |
| 28. C2×#108 | D3 | semidirect |
| 67. #108 | C2×D3 | semidirect |
| 151. C2×C3 | #430 | semidirect |
| 167. C3 | C2×#430 | semidirect |
| 171. C2 | #4893 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×M16 | 2 |
| C22×ΓL(1,𝔽25) | 2 |
| C2×C3×#108 | 2 |
| C2×#822 | 2 |
| C2×#819 | 2 |
| #4893 | 2 |
| C2×#430 | 3 |