Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
276 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 67 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. C2×#824 | C2 | semidirect |
| 5. #5120 | C2 | semidirect |
| 6. #5102 | C2 | semidirect |
| 7. C3×#341 | C2 | semidirect |
| 30. #341 | D3 | semidirect |
| 195. C3 | #2046 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#204 | 2 |
| C2×#824 | 2 |
| #5131 | 2 |
| C2×#823 | 2 |
| #5120 | 2 |
| #5102 | 2 |
| C3×#341 | 2 |
| #2046 | 3 |