Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
410 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 113 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. C2×#947 | C2 | semidirect |
| 2. #5624 | C2 | semidirect |
| 3. C3×#451 | C2 | semidirect |
| 4. #5227 | C2 | semidirect |
| 5. #5191 | C2 | semidirect |
| 6. #5185 | C2 | semidirect |
| 7. #5046 | C2 | semidirect |
| 8. #4819 | C2 | semidirect |
| 9. #4800 | C2 | semidirect |
| 11. #4718 | C2 | semidirect |
| 15. C2×C3×Q16 | C22 | semidirect |
| 21. #947 | C22 | semidirect |
| 22. Q8×Dic3 | C22 | semidirect |
| 24. C2×#215 | C22 | semidirect |
| 31. #893 | C22 | semidirect |
| 33. #890 | C22 | semidirect |
| 36. C3×#103 | C22 | semidirect |
| 38. #835 | C22 | semidirect |
| 41. Dic3⋊C8 | C22 | semidirect |
| 42. C8×Dic3 | C22 | semidirect |
| 50. #451 | D3 | semidirect |
| 98. C2×Q16 | C2×D3 | semidirect |
| 121. #103 | C2×D3 | semidirect |
| 280. C3 | #3211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#947 | 2 |
| #5624 | 2 |
| C3×#451 | 2 |
| #5227 | 2 |
| #5191 | 2 |
| #5185 | 2 |
| #5046 | 2 |
| #4819 | 2 |
| #4800 | 2 |
| #4732 | 2 |
| #4718 | 2 |
| #3211 | 3 |