Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
410 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 121 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×#124 | C2 | semidirect |
| 2. #5479 | C2 | semidirect |
| 3. #5228 | C2 | semidirect |
| 4. #5227 | C2 | semidirect |
| 5. #5218 | C2 | semidirect |
| 7. #5059 | C2 | semidirect |
| 8. #5057 | C2 | semidirect |
| 9. #5056 | C2 | semidirect |
| 10. #5054 | C2 | semidirect |
| 11. #4925 | C2 | semidirect |
| 22. C2×#216 | C22 | semidirect |
| 23. C2×#215 | C22 | semidirect |
| 31. #875 | C22 | semidirect |
| 32. C4×D12 | C22 | semidirect |
| 34. #870 | C22 | semidirect |
| 35. C4×Dic6 | C22 | semidirect |
| 36. #835 | C22 | semidirect |
| 37. #835 | C22 | semidirect |
| 42. C4⋊(C3⋊C8) | C22 | semidirect |
| 43. C4×C3⋊C8 | C22 | semidirect |
| 45. C2×#124 | 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×C3×#124 | 2 |
| #5479 | 2 |
| #5228 | 2 |
| #5227 | 2 |
| #5218 | 2 |
| #5217 | 2 |
| #5059 | 2 |
| #5057 | 2 |
| #5056 | 2 |
| #5054 | 2 |
| #4925 | 2 |
| #3211 | 3 |