Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
316 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 97 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×#833 | C2 | semidirect |
| 3. #5215 | C2 | semidirect |
| 4. C2×#819 | C2 | semidirect |
| 5. #5101 | C2 | semidirect |
| 11. C2×C3×D8 | C4 | semidirect |
| 53. C2×D8 | Dic3 | semidirect |
| 157. C3 | #1978 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×D8 | 2 |
| C2×#833 | 2 |
| #5215 | 2 |
| C2×#819 | 2 |
| #5101 | 2 |
| #1978 | 3 |