Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
344 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 83 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. #5516 | C2 | semidirect |
| 5. C2×#824 | C2 | semidirect |
| 6. #4555 | C2 | semidirect |
| 7. #4532 | C2 | semidirect |
| 15. #936 | C4 | semidirect |
| 207. C3 | #1888 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#936 | 2 |
| #5516 | 2 |
| C3×#418 | 2 |
| #5215 | 2 |
| C2×#824 | 2 |
| #4555 | 2 |
| #4532 | 2 |
| #1888 | 3 |