Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
484 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 131 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×#918 | C2 | semidirect |
| 3. C4×D3×Q8 | C2 | semidirect |
| 4. C3×#462 | C2 | semidirect |
| 5. #5185 | C2 | semidirect |
| 6. #5090 | C2 | semidirect |
| 7. #5027 | C2 | semidirect |
| 8. #4848 | C2 | semidirect |
| 9. #4837 | C2 | semidirect |
| 10. #4803 | C2 | semidirect |
| 11. #4798 | C2 | semidirect |
| 51. #462 | D3 | semidirect |
| 61. D3×Q8 | D4 | semidirect |
| 221. C3×C4 | #137 | semidirect |
| 284. C4 | #918 | semidirect |
| 287. C3 | #3037 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#918 | 2 |
| #5725 | 2 |
| C4×D3×Q8 | 2 |
| C3×#462 | 2 |
| #5185 | 2 |
| #5090 | 2 |
| #5027 | 2 |
| #4848 | 2 |
| #4837 | 2 |
| #4803 | 2 |
| #4798 | 2 |
| #3037 | 3 |