Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
812 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 812 conjugacy classes of subgroups — too many to draw. Only its 181 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×#41 | C2 | semidirect |
| 2. C22×#215 | C2 | semidirect |
| 3. C22×#213 | C2 | semidirect |
| 4. C2×#930 | C2 | semidirect |
| 5. #5238 | C2 | direct (N × H) |
| 6. C2×#835 | C2 | semidirect |
| 7. C2×#832 | C2 | semidirect |
| 8. C2×#830 | C2 | semidirect |
| 13. C2×C3×#41 | C22 | semidirect |
| 22. C2×#215 | C22 | semidirect |
| 24. C2×#213 | C22 | semidirect |
| 26. #930 | C22 | semidirect |
| 31. #835 | C22 | semidirect |
| 32. #832 | C22 | semidirect |
| 33. #830 | C22 | semidirect |
| 34. C22×#41 | D3 | semidirect |
| 50. C2×C3×Q8 | D4 | semidirect |
| 56. C2×C3×D4 | D4 | semidirect |
| 86. C2×#41 | C2×D3 | semidirect |
| 122. C3×Q8 | C2×D4 | semidirect |
| 126. C3×D4 | C2×D4 | semidirect |
| 155. C2×Q8 | #67 | semidirect |
| 167. C2×D4 | #67 | semidirect |
| 225. Q8 | C2×#67 | semidirect |
| 233. D4 | C2×#67 | semidirect |
| 252. C2×C3 | #449 | semidirect |
| 279. C3 | C2×#449 | semidirect |
| 283. C2 | #5238 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×#41 | 2 |
| C22×#215 | 2 |
| C22×#213 | 2 |
| C2×#930 | 2 |
| #5238 | 2 |
| C2×#835 | 2 |
| C2×#832 | 2 |
| C2×#830 | 2 |
| C2×#449 | 3 |