Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
410 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 3. #5137 | C2 | semidirect |
| 4. #4739 | C2 | semidirect |
| 5. #4721 | C2 | semidirect |
| 17. C2×Dic12 | C22 | semidirect |
| 19. #817 | C22 | semidirect |
| 20. #816 | C22 | semidirect |
| 144. C3 | #3195 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#924 | 2 |
| C3×#407 | 2 |
| #5137 | 2 |
| #4739 | 2 |
| #4721 | 2 |
| #3195 | 3 |