Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
406 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 406 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×#869 | C2 | semidirect |
| 4. C2×#810 | C2 | semidirect |
| 5. #4524 | C2 | semidirect |
| 71. C2×C3×C4 | SD16 | semidirect |
| 141. C2×C4 | #214 | semidirect |
| 168. C3 | #2013 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#214 | 2 |
| C2×#869 | 2 |
| C3×#390 | 2 |
| C2×#810 | 2 |
| #4524 | 2 |
| #2013 | 3 |