Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
126 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 39 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. C3×C22⋊C16 | C2 | semidirect |
| 3. #4551 | C2 | semidirect |
| 8. C2×D24 | C4 | semidirect |
| 11. #818 | C4 | semidirect |
| 13. C22⋊C16 | D3 | semidirect |
| 112. C3 | #1347 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5115 | 2 |
| C3×C22⋊C16 | 2 |
| #4551 | 2 |
| #1347 | 3 |