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×#915 | C2 | semidirect |
| 3. C4×D3×Q8 | C2 | semidirect |
| 4. C3×#460 | C2 | semidirect |
| 5. #5166 | C2 | semidirect |
| 6. #5075 | C2 | semidirect |
| 7. #5031 | C2 | semidirect |
| 8. #4849 | C2 | semidirect |
| 9. #4837 | C2 | semidirect |
| 10. #4771 | C2 | semidirect |
| 11. #4767 | C2 | semidirect |
| 53. #460 | D3 | semidirect |
| 63. D3×Q8 | D4 | semidirect |
| 220. C3×C4 | #137 | semidirect |
| 284. C4 | #915 | 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×#915 | 2 |
| #5716 | 2 |
| C4×D3×Q8 | 2 |
| C3×#460 | 2 |
| #5166 | 2 |
| #5075 | 2 |
| #5031 | 2 |
| #4849 | 2 |
| #4837 | 2 |
| #4771 | 2 |
| #4767 | 2 |
| #3037 | 3 |