Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
752 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 229 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 |
|---|---|---|
| 4. C2×C3×#103 | C2 | semidirect |
| 5. C2×#835 | C2 | semidirect |
| 6. C2×#816 | C2 | semidirect |
| 7. C2×#810 | C2 | semidirect |
| 8. #4802 | C2 | direct (N × H) |
| 13. C2×D3×Q8 | C4 | semidirect |
| 29. C3×#103 | C22 | semidirect |
| 30. #835 | C22 | semidirect |
| 31. #816 | C22 | semidirect |
| 32. #810 | C22 | semidirect |
| 40. C2×#103 | D3 | semidirect |
| 54. D3×Q8 | C2×C4 | semidirect |
| 100. #103 | C2×D3 | semidirect |
| 218. C2×C3 | #419 | semidirect |
| 239. C3 | C2×#419 | semidirect |
| 241. C2 | #4802 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D3×Q8 | 2 |
| C22×ΓL(1,𝔽25) | 2 |
| C2×#892 | 2 |
| C2×C3×#103 | 2 |
| C2×#835 | 2 |
| C2×#816 | 2 |
| C2×#810 | 2 |
| #4802 | 2 |
| C2×#419 | 3 |