Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
528 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 189 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. #5521 | C2 | semidirect |
| 3. C3×#405 | C2 | semidirect |
| 4. #5131 | C2 | semidirect |
| 5. #5106 | C2 | semidirect |
| 6. #4711 | C2 | semidirect |
| 7. C4×D24 | C2 | semidirect |
| 14. C2×D24 | C4 | semidirect |
| 19. C4×D12 | C22 | semidirect |
| 20. C3×#97 | C22 | semidirect |
| 21. C3×C4×C8 | C22 | semidirect |
| 22. #821 | C22 | semidirect |
| 23. #818 | C22 | semidirect |
| 24. #817 | C22 | semidirect |
| 31. #405 | D3 | semidirect |
| 36. C2×D12 | C2×C4 | semidirect |
| 40. C2×C3×C8 | C2×C4 | semidirect |
| 51. D24 | C2×C4 | semidirect |
| 52. D24 | C2×C4 | semidirect |
| 67. #97 | C2×D3 | semidirect |
| 68. C4×C8 | C2×D3 | semidirect |
| 96. C2×C8 | C4×D3 | semidirect |
| 150. C3 | #2948 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D24 | 2 |
| #5521 | 2 |
| C3×#405 | 2 |
| #5131 | 2 |
| #5106 | 2 |
| #4711 | 2 |
| C4×D24 | 2 |
| #2948 | 3 |