Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
388 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 125 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. #5579 | C2 | semidirect |
| 3. C3×C4×SD16 | C2 | semidirect |
| 4. #5171 | C2 | semidirect |
| 5. #5020 | C2 | semidirect |
| 6. #5008 | C2 | semidirect |
| 7. D3×#106 | C2 | semidirect |
| 8. #4805 | C2 | semidirect |
| 9. #4777 | C2 | semidirect |
| 10. C8×D12 | C2 | semidirect |
| 11. #4680 | C2 | semidirect |
| 50. C4×SD16 | D3 | semidirect |
| 132. D12 | SD16 | semidirect |
| 140. C3×C8 | #41 | semidirect |
| 218. C8 | #235 | semidirect |
| 241. C3 | #3335 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5579 | 2 |
| #5551 | 2 |
| C3×C4×SD16 | 2 |
| #5171 | 2 |
| #5020 | 2 |
| #5008 | 2 |
| D3×#106 | 2 |
| #4805 | 2 |
| #4777 | 2 |
| C8×D12 | 2 |
| #4680 | 2 |
| #3335 | 3 |