Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
404 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 123 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. #5567 | C2 | semidirect |
| 3. C3×#460 | C2 | semidirect |
| 4. #5175 | C2 | semidirect |
| 5. #5162 | C2 | semidirect |
| 6. #5076 | C2 | semidirect |
| 7. C4×#215 | C2 | semidirect |
| 8. #4841 | C2 | semidirect |
| 9. #4830 | C2 | semidirect |
| 10. #4762 | C2 | semidirect |
| 11. #4758 | C2 | semidirect |
| 49. #460 | D3 | semidirect |
| 143. Dic6 | SD16 | semidirect |
| 146. C3⋊C8 | #41 | semidirect |
| 251. C3 | #3392 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5718 | 2 |
| #5567 | 2 |
| C3×#460 | 2 |
| #5175 | 2 |
| #5162 | 2 |
| #5076 | 2 |
| C4×#215 | 2 |
| #4841 | 2 |
| #4830 | 2 |
| #4762 | 2 |
| #4758 | 2 |
| #3392 | 3 |