Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
334 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 121 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. C2×#870 | C2 | semidirect |
| 3. C3×#431 | C2 | semidirect |
| 4. #4847 | C2 | semidirect |
| 5. #4829 | C2 | semidirect |
| 8. #4722 | C2 | semidirect |
| 9. #4721 | C2 | semidirect |
| 10. #4697 | C2 | semidirect |
| 11. #4683 | C2 | semidirect |
| 54. #431 | D3 | semidirect |
| 245. C3 | #3232 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5479 | 2 |
| C2×#870 | 2 |
| C3×#431 | 2 |
| #4847 | 2 |
| #4829 | 2 |
| #4736 | 2 |
| #4735 | 2 |
| #4722 | 2 |
| #4721 | 2 |
| #4697 | 2 |
| #4683 | 2 |
| #3232 | 3 |