Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
784 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 165 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×C3×H(5,𝔽2) | C2 | semidirect |
| 2. #5830 | C2 | semidirect |
| 3. C2×#949 | C2 | semidirect |
| 4. C22×#213 | C2 | semidirect |
| 5. #5238 | C2 | semidirect |
| 6. #5234 | C2 | semidirect |
| 7. #5233 | C2 | semidirect |
| 8. #5217 | C2 | semidirect |
| 9. #5215 | C2 | semidirect |
| 16. C2×C3×#41 | C22 | semidirect |
| 20. C22×C3×D4 | C22 | semidirect |
| 21. C22×D12 | C22 | semidirect |
| 24. C2×#215 | C22 | semidirect |
| 28. C2×#213 | C22 | semidirect |
| 29. C2×#213 | C22 | semidirect |
| 30. #930 | C22 | semidirect |
| 31. #926 | C22 | semidirect |
| 32. C2×#208 | C22 | semidirect |
| 33. C22×C3⋊C8 | C22 | semidirect |
| 34. #835 | C22 | semidirect |
| 35. #832 | C22 | semidirect |
| 36. #832 | C22 | semidirect |
| 37. #830 | C22 | semidirect |
| 38. C2×H(5,𝔽2) | D3 | semidirect |
| 56. C3×#41 | D4 | semidirect |
| 70. C2×C3×D4 | D4 | semidirect |
| 98. C2×#41 | C2×D3 | semidirect |
| 103. C22×D4 | C2×D3 | semidirect |
| 170. #41 | #67 | semidirect |
| 189. C2×D4 | #67 | semidirect |
| 295. C3 | #3008 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×H(5,𝔽2) | 2 |
| #5830 | 2 |
| C2×#949 | 2 |
| C22×#213 | 2 |
| #5238 | 2 |
| #5234 | 2 |
| #5233 | 2 |
| #5217 | 2 |
| #5215 | 2 |
| #3008 | 3 |