Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
132 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 45 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. C3×#358 | C2 | semidirect |
| 4. #4564 | C2 | semidirect |
| 6. #4504 | C2 | semidirect |
| 7. #4490 | C2 | semidirect |
| 25. #358 | D3 | semidirect |
| 126. C3 | #2237 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5188 | 2 |
| #4880 | 2 |
| C3×#358 | 2 |
| #4564 | 2 |
| (C2×D3)⋊C16 | 2 |
| #4504 | 2 |
| #4490 | 2 |
| #2237 | 3 |