Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
532 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 165 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×#909 | C2 | semidirect |
| 2. C22×Dic12 | C2 | semidirect |
| 4. #5526 | C2 | semidirect |
| 5. C3×#405 | C2 | semidirect |
| 6. #4715 | C2 | semidirect |
| 7. #4699 | C2 | semidirect |
| 8. #4696 | C2 | semidirect |
| 38. #405 | D3 | semidirect |
| 188. C3 | #3156 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#909 | 2 |
| C22×Dic12 | 2 |
| C2×#904 | 2 |
| #5526 | 2 |
| C3×#405 | 2 |
| #4715 | 2 |
| #4699 | 2 |
| #4696 | 2 |
| #3156 | 3 |