Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
738 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 249 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 |
|---|---|---|
| 2. C3×C4×#41 | C2 | semidirect |
| 3. #5819 | C2 | semidirect |
| 4. #5005 | C2 | semidirect |
| 5. C2×#805 | C2 | semidirect |
| 8. #1010 | C4 | semidirect |
| 9. #1009 | C4 | semidirect |
| 16. C3×#117 | C22 | semidirect |
| 17. C2×C3×C42 | C22 | semidirect |
| 19. C2×#208 | C22 | semidirect |
| 20. #805 | C22 | semidirect |
| 21. #805 | C22 | semidirect |
| 24. C4×#41 | D3 | semidirect |
| 40. #235 | C2×C4 | semidirect |
| 42. C2×D12 | C2×C4 | semidirect |
| 44. C2×Dic6 | C2×C4 | semidirect |
| 64. #117 | C2×D3 | semidirect |
| 65. C2×C42 | C2×D3 | semidirect |
| 162. C3 | #2901 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5964 | 2 |
| C3×C4×#41 | 2 |
| #5819 | 2 |
| #5005 | 2 |
| C2×#805 | 2 |
| #2901 | 3 |