Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
528 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 181 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×#427 | C2 | semidirect |
| 4. #5101 | C2 | semidirect |
| 5. #5001 | C2 | semidirect |
| 6. #4872 | C2 | semidirect |
| 7. #4869 | C2 | semidirect |
| 14. C2×D24 | C4 | semidirect |
| 17. #893 | C22 | semidirect |
| 20. C3×#107 | C22 | semidirect |
| 21. C3×#106 | C22 | semidirect |
| 22. #815 | C22 | semidirect |
| 23. C8×Dic3 | C22 | semidirect |
| 24. #809 | C22 | semidirect |
| 29. #427 | D3 | semidirect |
| 36. C2×D12 | C2×C4 | semidirect |
| 39. C2×C3×C8 | C2×C4 | semidirect |
| 51. D24 | C2×C4 | semidirect |
| 52. D24 | C2×C4 | semidirect |
| 64. #107 | C2×D3 | semidirect |
| 65. #106 | C2×D3 | semidirect |
| 97. 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×#427 | 2 |
| #5101 | 2 |
| #5001 | 2 |
| #4872 | 2 |
| #4869 | 2 |
| #2948 | 3 |