Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
186 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 57 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. C3×#498 | C2 | semidirect |
| 2. #5092 | C2 | semidirect |
| 5. #5079 | C2 | semidirect |
| 7. #4454 | C2 | semidirect |
| 22. #498 | D3 | semidirect |
| 132. C3 | #1720 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#498 | 2 |
| #5092 | 2 |
| #5088 | 2 |
| #5079 | 2 |
| #4694 | 2 |
| #4454 | 2 |
| #1720 | 3 |